Projective Differential Geometry Old and New
Projective Differential Geometry Old and New
From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups
December 2004
Available
Hardback
9780521831864
$142.00
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eBook
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.
- Presents and summarizes recent research scattered in mathematical journals, and features historical, cultural and bibliographical comments collected at the end of each section
- Numerous exercises help the reader to master basic techniques and make it possible to avoid lengthy computation in the text of the book
- A unique feature of this book is that it puts classical projective differential geometry into a broader mathematical context and connects it with contemporary mathematics and mathematical physics
Reviews & endorsements
"... [a] remarkable book [with] absolute autonomy and a priceless tool for students and researchers. Moreover, the writing style used here makes the reading truly enjoyable and enlightening."
Laurent Guieu, Mathematical Reviews
Product details
December 2004Hardback
9780521831864
262 pages
235 × 160 × 20 mm
0.497kg
53 b/w illus. 35 exercises
Available
Table of Contents
- 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.
