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, UK ; New York :
Cambridge University Press,
2005.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
165. |
| Schlagworte: | |
| Online-Zugang: | 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 resource (xi, 249 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 236-246) and index. |
| ISBN: | 9780511265785 0511265786 0521831865 9780521831864 0511263503 9780511263507 0511265069 9780511265068 9780511543142 051154314X |
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| 505 | 0 | 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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| 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. |
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| series2 | Cambridge tracts in mathematics ; |
| spelling | Ovsienko, Valentin. http://id.loc.gov/authorities/names/n2003003680 Projective differential geometry old and new : from the Schwarzian derivative to the cohomology of diffeomorphism groups / V. Ovsienko, S. Tabachnikov. Cambridge, UK ; New York : Cambridge University Press, 2005. 1 online resource (xi, 249 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 165 Includes bibliographical references (pages 236-246) and index. Print version record. 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. http://id.loc.gov/authorities/subjects/sh85054147 Géométrie différentielle projective. MATHEMATICS Geometry Differential. bisacsh Projective differential geometry fast Tabachnikov, Serge. http://id.loc.gov/authorities/names/no96016527 has work: Projective differential geometry old and new (Text) https://id.oclc.org/worldcat/entity/E39PCFrVMP4d9JBHWqXBdwFmMP https://id.oclc.org/worldcat/ontology/hasWork Print version: Ovsienko, Valentin. Projective differential geometry old and new. Cambridge, UK ; New York : Cambridge University Press, 2005 0521831865 9780521831864 (DLC) 2004045919 (OCoLC)54953058 Cambridge tracts in mathematics ; 165. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=181813 Volltext |
| spellingShingle | Ovsienko, Valentin Projective differential geometry old and new : from the Schwarzian derivative to the cohomology of diffeomorphism groups / Cambridge tracts in mathematics ; 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. http://id.loc.gov/authorities/subjects/sh85054147 Géométrie différentielle projective. MATHEMATICS Geometry Differential. bisacsh Projective differential geometry fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85054147 |
| title | Projective differential geometry old and new : from the Schwarzian derivative to the cohomology of diffeomorphism groups / |
| title_alt | 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. http://id.loc.gov/authorities/subjects/sh85054147 Géométrie différentielle projective. MATHEMATICS Geometry Differential. bisacsh Projective differential geometry fast |
| topic_facet | Projective differential geometry. Géométrie différentielle projective. MATHEMATICS Geometry Differential. Projective differential geometry |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=181813 |
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