Lectures on the Topology of 3-Manifolds :: an Introduction to the Casson Invariant.
This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physi...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
2011.
|
| Ausgabe: | 2nd ed. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds. |
| Beschreibung: | 1 online resource (219 pages) |
| ISBN: | 9783110250367 3110250365 |
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| 245 | 1 | 0 | |a Lectures on the Topology of 3-Manifolds : |b an Introduction to the Casson Invariant. |
| 250 | |a 2nd ed. | ||
| 260 | |a Berlin : |b De Gruyter, |c 2011. | ||
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| 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 <_ 1; 1.6 Seifert manifolds; 1.7 Heegaard diagrams; 1.8 Exercises; 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; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises. | |
| 505 | 8 | |a 4 Even surgeries4.1 Exercises; 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; 5.4 Exercises; 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; 6.5 Exercises; 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. | |
| 505 | 8 | |a 7.7 Exercises8 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; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 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. | |
| 505 | 8 | |a 11.3 A surgery formula for the Rohlin invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 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 for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations. | |
| 505 | 8 | |a 16.3 Independence of Heegaard splitting16.4 Exercises; 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 boundary links; 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; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index. | |
| 520 | |a This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds. | ||
| 588 | 0 | |a Print version record. | |
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| 650 | 6 | |a Variétés topologiques à 3 dimensions. | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Three-manifolds (Topology) |2 fast | |
| 758 | |i has work: |a Lectures on the topology of 3-manifolds (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGRVVmYx48HXxqVGhkPbBP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Saveliev, Nikolai. |t Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant. |d Berlin : De Gruyter, ©2011 |z 9783110250350 |
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| _version_ | 1816881782623043584 |
| adam_text | |
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| author | Saveliev, Nikolai |
| author_facet | Saveliev, Nikolai |
| author_role | |
| author_sort | Saveliev, Nikolai |
| author_variant | n s ns |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA613 |
| callnumber-raw | QA613.2 .S288 2011 |
| callnumber-search | QA613.2 .S288 2011 |
| callnumber-sort | QA 3613.2 S288 42011 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| 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 <_ 1; 1.6 Seifert manifolds; 1.7 Heegaard diagrams; 1.8 Exercises; 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; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises. 4 Even surgeries4.1 Exercises; 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; 5.4 Exercises; 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; 6.5 Exercises; 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. 7.7 Exercises8 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; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 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 invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 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 for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations. 16.3 Independence of Heegaard splitting16.4 Exercises; 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 boundary links; 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; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index. |
| ctrlnum | (OCoLC)772845181 |
| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.34 |
| dewey-search | 514.34 |
| dewey-sort | 3514.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd ed. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn772845181 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:11Z |
| institution | BVB |
| isbn | 9783110250367 3110250365 |
| language | English |
| oclc_num | 772845181 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (219 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | De Gruyter, |
| record_format | marc |
| spelling | Saveliev, Nikolai. Lectures on the Topology of 3-Manifolds : an Introduction to the Casson Invariant. 2nd ed. Berlin : De Gruyter, 2011. 1 online resource (219 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier 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 <_ 1; 1.6 Seifert manifolds; 1.7 Heegaard diagrams; 1.8 Exercises; 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; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises. 4 Even surgeries4.1 Exercises; 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; 5.4 Exercises; 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; 6.5 Exercises; 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. 7.7 Exercises8 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; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 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 invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 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 for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations. 16.3 Independence of Heegaard splitting16.4 Exercises; 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 boundary links; 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; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index. This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds. Print version record. Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Three-manifolds (Topology) fast 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. Lectures on the Topology of 3-Manifolds : An Introduction to the Casson Invariant. Berlin : De Gruyter, ©2011 9783110250350 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430060 Volltext |
| spellingShingle | Saveliev, Nikolai Lectures on the Topology of 3-Manifolds : an Introduction to the Casson Invariant. 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 <_ 1; 1.6 Seifert manifolds; 1.7 Heegaard diagrams; 1.8 Exercises; 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; 2.5 Exercises; 3 Kirby calculus; 3.1 The linking number; 3.2 Kirby moves; 3.3 The linking matrix; 3.4 Reversing orientation; 3.5 Exercises. 4 Even surgeries4.1 Exercises; 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; 5.4 Exercises; 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; 6.5 Exercises; 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. 7.7 Exercises8 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; 8.6 Open book decompositions; 8.7 Exercises; 9 The Arf-invariant; 9.1 The Arf-invariant of a quadratic form; 9.2 The Arf-invariant of a knot; 9.3 Exercises; 10 Rohlin's theorem; 10.1 Characteristic surfaces; 10.2 The definition of q~; 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 invariant11.4 The homology cobordism group; 11.5 Exercises; 12 The Casson invariant; 12.1 Exercises; 13 The group SU (2); 13.1 Exercises; 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 for Seifert homology spheres; 14.6 Exercises; 15 The local properties of representation spaces; 15.1 Exercises; 16 Casson's invariant for Heegaard splittings; 16.1 The intersection product; 16.2 The orientations. 16.3 Independence of Heegaard splitting16.4 Exercises; 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 boundary links; 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; 18.3 Exercises; 19 The Casson invariant of Seifert manifolds; 19.1 The space R(S (p, q, r)); 19.2 Calculation of the Casson invariant; 19.3 Exercises; Conclusion; Bibliography; Index. Three-manifolds (Topology) http://id.loc.gov/authorities/subjects/sh85135028 Variétés topologiques à 3 dimensions. MATHEMATICS Topology. bisacsh Three-manifolds (Topology) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85135028 |
| 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. |
| title_fullStr | Lectures on the Topology of 3-Manifolds : an Introduction to the Casson Invariant. |
| title_full_unstemmed | Lectures on the Topology of 3-Manifolds : an Introduction to the Casson Invariant. |
| 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 |
| topic_facet | Three-manifolds (Topology) Variétés topologiques à 3 dimensions. MATHEMATICS Topology. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430060 |
| work_keys_str_mv | AT savelievnikolai lecturesonthetopologyof3manifoldsanintroductiontothecassoninvariant |