Algebraic models in geometry

Yves Félix, John Oprea, Daniel Tanré019920652X, 9780199206520, 9781435656390, 9780199206513, 0199206511

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kahler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods.

---

Table of contents :
Algebraic Models in Geometry……Page 4
Preface……Page 8
Contents……Page 16
1 Lie groups and homogeneous spaces……Page 24
2 Minimal models……Page 79
3 Manifolds……Page 127
4 Complex and symplectic manifolds……Page 168
5 Geodesics……Page 228
6 Curvature……Page 262
7 G-spaces……Page 294
8 Blow-ups and Intersection Products……Page 340
9 A Florilège of geometric applications……Page 373
Appendix A De Rham forms……Page 415
Appendix B Spectral sequences……Page 432
Appendix C Basic homotopy recollections……Page 446
References……Page 456
Index……Page 474