Projective differential geometry old and new: from the Schwarzian derivative to the cohomology of diffeomorphism groups
Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and p...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2005
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| Schriftenreihe: | Cambridge tracts in mathematics
165 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject |
| Beschreibung: | 1 Online-Ressource (xi, 249 Seiten) |
| ISBN: | 9780511543142 |
| DOI: | 10.1017/CBO9780511543142 |
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| 245 | 1 | 0 | |a Projective differential geometry old and new |b from the Schwarzian derivative to the cohomology of diffeomorphism groups |c V. Ovsienko, S. Tabachnikov |
| 246 | 1 | 3 | |a Projective Differential Geometry Old & New |
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| 505 | 8 | 0 | |g 1 |t Introduction |g 2 |t The Geometry of the projective line |g 3 |t The Algebra of the projective line and cohomology of Diff(S1) |g 4 |t Vertices of projective curves |g 5 |t Projective invariants of submanifolds |g 6 |t Projective structures on smooth manifolds |g 7 |t Multi-dimensional Schwarzian derivatives and differential operators |g Appendix 1 |t Five proofs of the Sturm theorem |g Appendix 2 |t The Language of symplectic and contact geometry |g Appendix 3 |t The Language of connections |g Appendix 4 |t The Language of homological algebra |g Appendix 5 |t Remarkable cocycles on groups of diffeomorphisms |g Appendix 6 |t The Godbillon-Vey class |g Appendix 7 |t The Adler-Gelfand-Dickey bracket and infinite-dimensional Poisson geometry |
| 520 | |a Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject | ||
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Datensatz im Suchindex
| _version_ | 1804176884117798912 |
|---|---|
| any_adam_object | |
| author | Ovsienko, Valentin 1964- |
| author_GND | (DE-588)138292973 (DE-588)133854604 |
| author_facet | Ovsienko, Valentin 1964- |
| author_role | aut |
| author_sort | Ovsienko, Valentin 1964- |
| author_variant | v o vo |
| building | Verbundindex |
| bvnumber | BV043941876 |
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| contents | Introduction The Geometry of the projective line The Algebra of the projective line and cohomology of Diff(S1) Vertices of projective curves Projective invariants of submanifolds Projective structures on smooth manifolds Multi-dimensional Schwarzian derivatives and differential operators Five proofs of the Sturm theorem The Language of symplectic and contact geometry The Language of connections The Language of homological algebra Remarkable cocycles on groups of diffeomorphisms The Godbillon-Vey class The Adler-Gelfand-Dickey bracket and infinite-dimensional Poisson geometry |
| ctrlnum | (ZDB-20-CBO)CR9780511543142 (OCoLC)850420465 (DE-599)BVBBV043941876 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543142 |
| format | Electronic eBook |
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| id | DE-604.BV043941876 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511543142 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350846 |
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| physical | 1 Online-Ressource (xi, 249 Seiten) |
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| publishDate | 2005 |
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| publisher | Cambridge University Press |
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| spelling | Ovsienko, Valentin 1964- Verfasser (DE-588)138292973 aut Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups V. Ovsienko, S. Tabachnikov Projective Differential Geometry Old & New Cambridge Cambridge University Press 2005 1 Online-Ressource (xi, 249 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 165 1 Introduction 2 The Geometry of the projective line 3 The Algebra of the projective line and cohomology of Diff(S1) 4 Vertices of projective curves 5 Projective invariants of submanifolds 6 Projective structures on smooth manifolds 7 Multi-dimensional Schwarzian derivatives and differential operators Appendix 1 Five proofs of the Sturm theorem Appendix 2 The Language of symplectic and contact geometry Appendix 3 The Language of connections Appendix 4 The Language of homological algebra Appendix 5 Remarkable cocycles on groups of diffeomorphisms Appendix 6 The Godbillon-Vey class Appendix 7 The Adler-Gelfand-Dickey bracket and infinite-dimensional Poisson geometry Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject Projective differential geometry Projektive Differentialgeometrie (DE-588)4175883-3 gnd rswk-swf Projektive Differentialgeometrie (DE-588)4175883-3 s DE-604 Tabachnikov, Serge 1956- Sonstige (DE-588)133854604 oth Erscheint auch als Druckausgabe 978-0-521-83186-4 https://doi.org/10.1017/CBO9780511543142 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ovsienko, Valentin 1964- Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups Introduction The Geometry of the projective line The Algebra of the projective line and cohomology of Diff(S1) Vertices of projective curves Projective invariants of submanifolds Projective structures on smooth manifolds Multi-dimensional Schwarzian derivatives and differential operators Five proofs of the Sturm theorem The Language of symplectic and contact geometry The Language of connections The Language of homological algebra Remarkable cocycles on groups of diffeomorphisms The Godbillon-Vey class The Adler-Gelfand-Dickey bracket and infinite-dimensional Poisson geometry Projective differential geometry Projektive Differentialgeometrie (DE-588)4175883-3 gnd |
| subject_GND | (DE-588)4175883-3 |
| title | Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups |
| title_alt | Projective Differential Geometry Old & New Introduction The Geometry of the projective line The Algebra of the projective line and cohomology of Diff(S1) Vertices of projective curves Projective invariants of submanifolds Projective structures on smooth manifolds Multi-dimensional Schwarzian derivatives and differential operators Five proofs of the Sturm theorem The Language of symplectic and contact geometry The Language of connections The Language of homological algebra Remarkable cocycles on groups of diffeomorphisms The Godbillon-Vey class The Adler-Gelfand-Dickey bracket and infinite-dimensional Poisson geometry |
| title_auth | Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups |
| title_exact_search | Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups |
| title_full | Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups V. Ovsienko, S. Tabachnikov |
| title_fullStr | Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups V. Ovsienko, S. Tabachnikov |
| title_full_unstemmed | Projective differential geometry old and new from the Schwarzian derivative to the cohomology of diffeomorphism groups V. Ovsienko, S. Tabachnikov |
| title_short | Projective differential geometry old and new |
| title_sort | projective differential geometry old and new from the schwarzian derivative to the cohomology of diffeomorphism groups |
| title_sub | from the Schwarzian derivative to the cohomology of diffeomorphism groups |
| topic | Projective differential geometry Projektive Differentialgeometrie (DE-588)4175883-3 gnd |
| topic_facet | Projective differential geometry Projektive Differentialgeometrie |
| url | https://doi.org/10.1017/CBO9780511543142 |
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