V. Ovsienko, Valentin Ovsienko, S. Tabachnikov

Projective Differential Geometry Old and New

From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups

• Gebundenes Buch

Produktbeschreibung

Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. This book provides a rapid route for graduate students and researchers to contemplate the frontiers of contemporary research in this classic subject. The authors include exercises and historical and cultural comments relating the basic ideas to a broader context.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 262
• Erscheinungstermin: 1. November 2010
• Englisch
• Abmessung: 235mm x 157mm x 20mm
• Gewicht: 583g
• ISBN-13: 9780521831864
• ISBN-10: 0521831865
• Artikelnr.: 22014257

Inhaltsangabe

Preface: why projective?
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
Bibliography
Index.