Algebraic Models in Geometry
Series: Oxford Graduate Texts in Mathematics;
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Product details:
- Publisher OUP Oxford
- Date of Publication 13 March 2008
- ISBN 9780199206520
- Binding Paperback
- No. of pages488 pages
- Size 234x156x27 mm
- Weight 738 g
- Language English
- Illustrations 138 line diagrams 0
Categories
Short description:
A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.
MoreLong description:
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 Kähler 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.
MoreTable of Contents:
Lie Groups and Homogeneous Spaces
Minimal Models
Manifolds
Complex and Symplectic Manifolds
Geodesics
Curvature
G-Spaces
Blow-ups and Intersection Products
A Florilège of Geometric Applications
Appendices
De Rham Forms
Spectral Sequences
Basic Homotopy Recollections
