Algebraic Models in Geometry - Félix, Yves; Oprea, John; Tanré, Daniel; - Prospero Internet Bookshop

Algebraic Models in Geometry
 
Product details:

ISBN13:9780199206520
ISBN10:019920652X
Binding:Paperback
No. of pages:488 pages
Size:234x156x27 mm
Weight:738 g
Language:English
Illustrations: 138 line diagrams
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Algebraic Models in Geometry

 
Publisher: OUP Oxford
Date of Publication:
 
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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.

Long 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.
Table of Contents:
Lie Groups and Homogeneous Spaces
Minimal Models
Manifolds
Complex and Symplectic Manifolds
Geodesics
Curvature
G-Spaces
Blow-ups and Intersection Products
A Floril?ge of Geometric Applications
Appendices
De Rham Forms
Spectral Sequences
Basic Homotopy Recollections