Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups

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.