Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups
Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups
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射影微分几何的新与旧：从施瓦茨导数到微分同胚群的上同调
DOI：
10.1017/cbo9780511543142
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
S. Tabachnikov
中科院分区：
文献类型：
--
作者：
V. Ovsienko;S. Tabachnikov
前言：为什么是投影？1. 介绍2。投影线的几何形状。Diff(S1) 4的射影线代数与上同调。投影曲线的顶点子流形的射影不变量光滑流形上的投影结构多维Schwarzian导数和微分算子。Sturm定理的五个证明（附录2）。辛几何和接触几何的语言。连接语言附录4。同调代数的语言。附录5。差分同态群上的显著环。goldlion - vey类Adler-Gelfand-Dickey括号和无限维泊松几何书目索引。
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.