Lectures on the topology of 3-manifolds :: an introduction to the Casson invariant /
"Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-invariant. The...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York :
Walter de Gruyter,
1999.
|
| Schriftenreihe: | De Gruyter textbook.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-invariant. The purpose of this book is to provide a much-needed bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in low-dimensional topology and gauge theory." "The text will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds."--Jacket |
| Beschreibung: | 1 online resource (ix, 199 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 186-195) and index. |
| ISBN: | 9783110806359 3110806355 |
Internformat
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| 100 | 1 | |a Saveliev, Nikolai, |d 1966- |1 https://id.oclc.org/worldcat/entity/E39PCjwqfXvBb8vqJRXBfg9wbq |0 http://id.loc.gov/authorities/names/n99052266 | |
| 245 | 1 | 0 | |a Lectures on the topology of 3-manifolds : |b an introduction to the Casson invariant / |c Nikolaĭ Saveliev. |
| 264 | 1 | |a Berlin ; |a New York : |b Walter de Gruyter, |c 1999. | |
| 300 | |a 1 online resource (ix, 199 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a De Gruyter textbook | |
| 504 | |a Includes bibliographical references (pages 186-195) and index. | ||
| 520 | 1 | |a "Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-invariant. The purpose of this book is to provide a much-needed bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in low-dimensional topology and gauge theory." "The text will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds."--Jacket | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface -- Introduction -- Glossary -- 1 Heegaard Splittings -- 1.1 Introduction -- 1.2 Existence Of Heegaard Splittings -- 1.3 Stable Equivalence Of Heegaard Splittings -- 1.4 The Mapping Class Group -- 1.5 Manifolds Of Heegaard Genus â?? 1 -- 1.6 Seifert Manifolds -- 2 Dehn Surgery -- 2.1 Knots And Links In 3-Manifolds -- 2.2 Surgery On Links In S3 -- 2.3 Surgery Description Of Lens Spaces And Seifert Manifolds -- 2.4 Surgery And 4-Manifolds -- 3 Kirby Calculus -- 3.1 The Linking Number -- 3.2 Kirby Moves -- 3.3 The Linking Matrix | |
| 505 | 8 | |a 3.4 Reversing Orientation 4 Even Surgeries -- 5 Review Of 4-Manifolds -- 5.1 Definition Of The Intersection Form -- 5.2 The Unimodular Integral Forms -- 5.3 Four-Manifolds And Intersection Forms -- 6 Four-Manifolds With Boundary -- 6.1 The Intersection Form -- 6.2 Homology Spheres Via Surgery On Knots -- 6.3 Seifert Homology Spheres -- 6.4 The Rohlin Invariant -- 7 Invariants Of Knots And Links -- 7.1 Seifert Surfaces -- 7.2 Seifert Matrices -- 7.3 The Alexander Polynomial -- 7.4 Other Invariants From Seifert Surfaces | |
| 505 | 8 | |a 7.5 Knots In Homology Spheres 7.6 Boundary Links And The Alexander Polynomial -- 8 Fibered Knots -- 8.1 The Definition Of A Fibered Knot -- 8.2 The Monodromy -- 8.3 More About Torus Knots -- 8.4 Joins -- 8.5 The Monodromy Of Torus Knots -- 9 The Arf-Invariant -- 9.1 The Arf-Invariant Of A Quadratic Form -- 9.2 The Arf-Invariant Of A Knot -- 10 Rohlinâ€?S Theorem -- 10.1 Characteristic Surfaces -- 10.2 The Definition Of QÌ? -- 10.3 Representing Homology Classes By Surfaces -- 11 The Rohlin Invariant | |
| 505 | 8 | |a 11.1 Definition Of The Rohlin Invariant 11.2 The Rohlin Invariant Of Seifert Spheres -- 11.3 A Surgery Formula For The Rohlin Invariant -- 11.4 The Homology Cobordism Group -- 12 The Casson Invariant -- 13 The Group Su(2) -- 14 Representation Spaces -- 14.1 The Topology Of Representation Spaces -- 14.2 Irreducible Representations -- 14.3 Representations Of Free Groups -- 14.4 Representations Of Surface Groups -- 14.5 Representations Of Seifert Homology Spheres -- 15 The Local Properties Of Representation Spaces | |
| 505 | 8 | |a 16 Casson�S Invariant For Heegaard Splittings 16.1 The Intersection Product -- 16.2 The Orientations -- 16.3 Independence Of Heegaard Splitting -- 17 Casson�S Invariant For Knots -- 17.1 Preferred Heegaard Splittings -- 17.2 The Casson Invariant For Knots -- 17.3 The Difference Cycle -- 17.4 The Casson Invariant For Unlinks -- 17.5 The Casson Invariant Of A Trefoil -- 18 An Application Of The Casson Invariant -- 18.1 Triangulating 4-Manifolds -- 18.2 Higher-Dimensional Manifolds -- 19 The Casson Invariant Of Seifert Manifolds | |
| 650 | 0 | |a Three-manifolds (Topology) |0 http://id.loc.gov/authorities/subjects/sh85135028 | |
| 650 | 6 | |a Variétés topologiques à 3 dimensions. | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Three-manifolds (Topology) |2 fast | |
| 650 | 7 | |a Casson-Invariante |2 gnd |0 http://d-nb.info/gnd/4314105-5 | |
| 650 | 7 | |a Mannigfaltigkeit |2 gnd |0 http://d-nb.info/gnd/4037379-4 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn857769509 |
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| _version_ | 1816882243826614272 |
| adam_text | |
| any_adam_object | |
| author | Saveliev, Nikolai, 1966- |
| author_GND | http://id.loc.gov/authorities/names/n99052266 |
| author_facet | Saveliev, Nikolai, 1966- |
| author_role | |
| author_sort | Saveliev, Nikolai, 1966- |
| author_variant | n s ns |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA613 |
| callnumber-raw | QA613.2 .S28 1999eb |
| callnumber-search | QA613.2 .S28 1999eb |
| callnumber-sort | QA 3613.2 S28 41999EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Preface -- Introduction -- Glossary -- 1 Heegaard Splittings -- 1.1 Introduction -- 1.2 Existence Of Heegaard Splittings -- 1.3 Stable Equivalence Of Heegaard Splittings -- 1.4 The Mapping Class Group -- 1.5 Manifolds Of Heegaard Genus â?? 1 -- 1.6 Seifert Manifolds -- 2 Dehn Surgery -- 2.1 Knots And Links In 3-Manifolds -- 2.2 Surgery On Links In S3 -- 2.3 Surgery Description Of Lens Spaces And Seifert Manifolds -- 2.4 Surgery And 4-Manifolds -- 3 Kirby Calculus -- 3.1 The Linking Number -- 3.2 Kirby Moves -- 3.3 The Linking Matrix 3.4 Reversing Orientation 4 Even Surgeries -- 5 Review Of 4-Manifolds -- 5.1 Definition Of The Intersection Form -- 5.2 The Unimodular Integral Forms -- 5.3 Four-Manifolds And Intersection Forms -- 6 Four-Manifolds With Boundary -- 6.1 The Intersection Form -- 6.2 Homology Spheres Via Surgery On Knots -- 6.3 Seifert Homology Spheres -- 6.4 The Rohlin Invariant -- 7 Invariants Of Knots And Links -- 7.1 Seifert Surfaces -- 7.2 Seifert Matrices -- 7.3 The Alexander Polynomial -- 7.4 Other Invariants From Seifert Surfaces 7.5 Knots In Homology Spheres 7.6 Boundary Links And The Alexander Polynomial -- 8 Fibered Knots -- 8.1 The Definition Of A Fibered Knot -- 8.2 The Monodromy -- 8.3 More About Torus Knots -- 8.4 Joins -- 8.5 The Monodromy Of Torus Knots -- 9 The Arf-Invariant -- 9.1 The Arf-Invariant Of A Quadratic Form -- 9.2 The Arf-Invariant Of A Knot -- 10 Rohlinâ€?S Theorem -- 10.1 Characteristic Surfaces -- 10.2 The Definition Of QÌ? -- 10.3 Representing Homology Classes By Surfaces -- 11 The Rohlin Invariant 11.1 Definition Of The Rohlin Invariant 11.2 The Rohlin Invariant Of Seifert Spheres -- 11.3 A Surgery Formula For The Rohlin Invariant -- 11.4 The Homology Cobordism Group -- 12 The Casson Invariant -- 13 The Group Su(2) -- 14 Representation Spaces -- 14.1 The Topology Of Representation Spaces -- 14.2 Irreducible Representations -- 14.3 Representations Of Free Groups -- 14.4 Representations Of Surface Groups -- 14.5 Representations Of Seifert Homology Spheres -- 15 The Local Properties Of Representation Spaces 16 Cassonâ€?S Invariant For Heegaard Splittings 16.1 The Intersection Product -- 16.2 The Orientations -- 16.3 Independence Of Heegaard Splitting -- 17 Cassonâ€?S Invariant For Knots -- 17.1 Preferred Heegaard Splittings -- 17.2 The Casson Invariant For Knots -- 17.3 The Difference Cycle -- 17.4 The Casson Invariant For Unlinks -- 17.5 The Casson Invariant Of A Trefoil -- 18 An Application Of The Casson Invariant -- 18.1 Triangulating 4-Manifolds -- 18.2 Higher-Dimensional Manifolds -- 19 The Casson Invariant Of Seifert Manifolds |
| ctrlnum | (OCoLC)857769509 |
| dewey-full | 514/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.3 |
| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn857769509 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:31Z |
| institution | BVB |
| isbn | 9783110806359 3110806355 |
| language | English |
| oclc_num | 857769509 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (ix, 199 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Walter de Gruyter, |
| record_format | marc |
| series | De Gruyter textbook. |
| series2 | De Gruyter textbook |
| spelling | Saveliev, Nikolai, 1966- https://id.oclc.org/worldcat/entity/E39PCjwqfXvBb8vqJRXBfg9wbq http://id.loc.gov/authorities/names/n99052266 Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / Nikolaĭ Saveliev. Berlin ; New York : Walter de Gruyter, 1999. 1 online resource (ix, 199 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file De Gruyter textbook Includes bibliographical references (pages 186-195) and index. "Progress in low-dimensional topology has been very fast in the last two decades, leading to the solutions of many difficult problems." "Among the highlights of this period are Casson's results on the Rohlin invariant of homotopy 3-spheres, as well as his [lambda]-invariant. The purpose of this book is to provide a much-needed bridge to these modern topics. The book covers some classical topics, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and gives a brief sketch of links with the latest developments in low-dimensional topology and gauge theory." "The text will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds."--Jacket Print version record. Preface -- Introduction -- Glossary -- 1 Heegaard Splittings -- 1.1 Introduction -- 1.2 Existence Of Heegaard Splittings -- 1.3 Stable Equivalence Of Heegaard Splittings -- 1.4 The Mapping Class Group -- 1.5 Manifolds Of Heegaard Genus â?? 1 -- 1.6 Seifert Manifolds -- 2 Dehn Surgery -- 2.1 Knots And Links In 3-Manifolds -- 2.2 Surgery On Links In S3 -- 2.3 Surgery Description Of Lens Spaces And Seifert Manifolds -- 2.4 Surgery And 4-Manifolds -- 3 Kirby Calculus -- 3.1 The Linking Number -- 3.2 Kirby Moves -- 3.3 The Linking Matrix 3.4 Reversing Orientation 4 Even Surgeries -- 5 Review Of 4-Manifolds -- 5.1 Definition Of The Intersection Form -- 5.2 The Unimodular Integral Forms -- 5.3 Four-Manifolds And Intersection Forms -- 6 Four-Manifolds With Boundary -- 6.1 The Intersection Form -- 6.2 Homology Spheres Via Surgery On Knots -- 6.3 Seifert Homology Spheres -- 6.4 The Rohlin Invariant -- 7 Invariants Of Knots And Links -- 7.1 Seifert Surfaces -- 7.2 Seifert Matrices -- 7.3 The Alexander Polynomial -- 7.4 Other Invariants From Seifert Surfaces 7.5 Knots In Homology Spheres 7.6 Boundary Links And The Alexander Polynomial -- 8 Fibered Knots -- 8.1 The Definition Of A Fibered Knot -- 8.2 The Monodromy -- 8.3 More About Torus Knots -- 8.4 Joins -- 8.5 The Monodromy Of Torus Knots -- 9 The Arf-Invariant -- 9.1 The Arf-Invariant Of A Quadratic Form -- 9.2 The Arf-Invariant Of A Knot -- 10 Rohlinâ€?S Theorem -- 10.1 Characteristic Surfaces -- 10.2 The Definition Of QÌ? -- 10.3 Representing Homology Classes By Surfaces -- 11 The Rohlin Invariant 11.1 Definition Of The Rohlin Invariant 11.2 The Rohlin Invariant Of Seifert Spheres -- 11.3 A Surgery Formula For The Rohlin Invariant -- 11.4 The Homology Cobordism Group -- 12 The Casson Invariant -- 13 The Group Su(2) -- 14 Representation Spaces -- 14.1 The Topology Of Representation Spaces -- 14.2 Irreducible Representations -- 14.3 Representations Of Free Groups -- 14.4 Representations Of Surface Groups -- 14.5 Representations Of Seifert Homology Spheres -- 15 The Local Properties Of Representation Spaces 16 Cassonâ€?S Invariant For Heegaard Splittings 16.1 The Intersection Product -- 16.2 The Orientations -- 16.3 Independence Of Heegaard Splitting -- 17 Cassonâ€?S Invariant For Knots -- 17.1 Preferred Heegaard Splittings -- 17.2 The Casson Invariant For Knots -- 17.3 The Difference Cycle -- 17.4 The Casson Invariant For Unlinks -- 17.5 The Casson Invariant Of A Trefoil -- 18 An Application Of The Casson Invariant -- 18.1 Triangulating 4-Manifolds -- 18.2 Higher-Dimensional Manifolds -- 19 The Casson Invariant Of Seifert Manifolds Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Three-manifolds (Topology) fast Casson-Invariante gnd http://d-nb.info/gnd/4314105-5 Mannigfaltigkeit gnd http://d-nb.info/gnd/4037379-4 Dimension 3 gnd http://d-nb.info/gnd/4321722-9 Topologie gnd http://d-nb.info/gnd/4060425-1 has work: Lectures on the topology of 3-manifolds (Text) https://id.oclc.org/worldcat/entity/E39PCGRVVmYx48HXxqVGhkPbBP https://id.oclc.org/worldcat/ontology/hasWork Print version: Saveliev, Nikolai, 1966- Lectures on the topology of 3-manifolds 3110162725 (DLC) 99040959 (OCoLC)41967193 De Gruyter textbook. http://id.loc.gov/authorities/names/n94049545 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=627747 Volltext |
| spellingShingle | Saveliev, Nikolai, 1966- Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / De Gruyter textbook. Preface -- Introduction -- Glossary -- 1 Heegaard Splittings -- 1.1 Introduction -- 1.2 Existence Of Heegaard Splittings -- 1.3 Stable Equivalence Of Heegaard Splittings -- 1.4 The Mapping Class Group -- 1.5 Manifolds Of Heegaard Genus â?? 1 -- 1.6 Seifert Manifolds -- 2 Dehn Surgery -- 2.1 Knots And Links In 3-Manifolds -- 2.2 Surgery On Links In S3 -- 2.3 Surgery Description Of Lens Spaces And Seifert Manifolds -- 2.4 Surgery And 4-Manifolds -- 3 Kirby Calculus -- 3.1 The Linking Number -- 3.2 Kirby Moves -- 3.3 The Linking Matrix 3.4 Reversing Orientation 4 Even Surgeries -- 5 Review Of 4-Manifolds -- 5.1 Definition Of The Intersection Form -- 5.2 The Unimodular Integral Forms -- 5.3 Four-Manifolds And Intersection Forms -- 6 Four-Manifolds With Boundary -- 6.1 The Intersection Form -- 6.2 Homology Spheres Via Surgery On Knots -- 6.3 Seifert Homology Spheres -- 6.4 The Rohlin Invariant -- 7 Invariants Of Knots And Links -- 7.1 Seifert Surfaces -- 7.2 Seifert Matrices -- 7.3 The Alexander Polynomial -- 7.4 Other Invariants From Seifert Surfaces 7.5 Knots In Homology Spheres 7.6 Boundary Links And The Alexander Polynomial -- 8 Fibered Knots -- 8.1 The Definition Of A Fibered Knot -- 8.2 The Monodromy -- 8.3 More About Torus Knots -- 8.4 Joins -- 8.5 The Monodromy Of Torus Knots -- 9 The Arf-Invariant -- 9.1 The Arf-Invariant Of A Quadratic Form -- 9.2 The Arf-Invariant Of A Knot -- 10 Rohlinâ€?S Theorem -- 10.1 Characteristic Surfaces -- 10.2 The Definition Of QÌ? -- 10.3 Representing Homology Classes By Surfaces -- 11 The Rohlin Invariant 11.1 Definition Of The Rohlin Invariant 11.2 The Rohlin Invariant Of Seifert Spheres -- 11.3 A Surgery Formula For The Rohlin Invariant -- 11.4 The Homology Cobordism Group -- 12 The Casson Invariant -- 13 The Group Su(2) -- 14 Representation Spaces -- 14.1 The Topology Of Representation Spaces -- 14.2 Irreducible Representations -- 14.3 Representations Of Free Groups -- 14.4 Representations Of Surface Groups -- 14.5 Representations Of Seifert Homology Spheres -- 15 The Local Properties Of Representation Spaces 16 Cassonâ€?S Invariant For Heegaard Splittings 16.1 The Intersection Product -- 16.2 The Orientations -- 16.3 Independence Of Heegaard Splitting -- 17 Cassonâ€?S Invariant For Knots -- 17.1 Preferred Heegaard Splittings -- 17.2 The Casson Invariant For Knots -- 17.3 The Difference Cycle -- 17.4 The Casson Invariant For Unlinks -- 17.5 The Casson Invariant Of A Trefoil -- 18 An Application Of The Casson Invariant -- 18.1 Triangulating 4-Manifolds -- 18.2 Higher-Dimensional Manifolds -- 19 The Casson Invariant Of Seifert Manifolds Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Three-manifolds (Topology) fast Casson-Invariante gnd http://d-nb.info/gnd/4314105-5 Mannigfaltigkeit gnd http://d-nb.info/gnd/4037379-4 Dimension 3 gnd http://d-nb.info/gnd/4321722-9 Topologie gnd http://d-nb.info/gnd/4060425-1 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85135028 http://d-nb.info/gnd/4314105-5 http://d-nb.info/gnd/4037379-4 http://d-nb.info/gnd/4321722-9 http://d-nb.info/gnd/4060425-1 |
| title | Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / |
| title_auth | Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / |
| title_exact_search | Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / |
| title_full | Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / Nikolaĭ Saveliev. |
| title_fullStr | Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / Nikolaĭ Saveliev. |
| title_full_unstemmed | Lectures on the topology of 3-manifolds : an introduction to the Casson invariant / Nikolaĭ Saveliev. |
| title_short | Lectures on the topology of 3-manifolds : |
| title_sort | lectures on the topology of 3 manifolds an introduction to the casson invariant |
| title_sub | an introduction to the Casson invariant / |
| topic | Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Three-manifolds (Topology) fast Casson-Invariante gnd http://d-nb.info/gnd/4314105-5 Mannigfaltigkeit gnd http://d-nb.info/gnd/4037379-4 Dimension 3 gnd http://d-nb.info/gnd/4321722-9 Topologie gnd http://d-nb.info/gnd/4060425-1 |
| topic_facet | Three-manifolds (Topology) Variétés topologiques à 3 dimensions. MATHEMATICS Topology. Casson-Invariante Mannigfaltigkeit Dimension 3 Topologie |
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| work_keys_str_mv | AT savelievnikolai lecturesonthetopologyof3manifoldsanintroductiontothecassoninvariant |