Algebraic Models in Geometry

Paperback | March 13, 2008

byYves Felix, John Oprea, Daniel Tanre

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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 togeometrical 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 centraltheme 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.

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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 togeometrical problems amenable to topological methods a...

Yves Felix, author of books on raional homotopy and more than eighty papers in algebraic topology, received his Ph.D. in 1979. From 1981 to 1989 he worked as a researcher for the FNRS (Belgium) and in 1989 he took up the position of Professor at the Universite Catholique de Louvain, which he has held since. John Oprea received his Ph....

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Format:PaperbackDimensions:304 pages, 9.21 × 6.14 × 1.06 inPublished:March 13, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019920652X

ISBN - 13:9780199206520

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Table of Contents

1. Lie Groups and Homogeneous Spaces2. Minimal Models3. Manifolds4. Complex and Symplectic Manifolds5. Geodesics6. Curvature7. G-Spaces8. Blow-ups and Intersection Products9. A Florilege of Geometric ApplicationsAppendicesA. De Rham FormsB. Spectral SequencesC. Basic Homotopy Recollections