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 K�hler 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.
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"An invaluable addition to the literature, surveying decades of vital research and taking the reader to the frontiers with countless open questions and paths into unexplored terrain."--Mathematical Reviews
About the Author
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 Universit� Catholique de Louvain, which he has held since. John Oprea received his Ph.D. in 1982 from Ohio State University and has been at Cleveland State University since 1985. His interests lie in both algebraic topology and differential geometry and he has written papers and books in these areas. Oprea was awarded the Lester R. Ford award from the Mathematical Association of America in 1996. He is currently an associate editor for the Journal of Geometry and Symmetry in Physics. Daniel Tanr� received his Ph. D. from the University of Paris in 1972 and has been a Professor at the University of Lille, France, since 1988. He has been an author of books and articles on Algebraic Topology and applications since 1972.
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First Sentence:
Lie groups and homogeneous spaces form an important family of examples of manifolds. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
shriek map, relative minimal model, bigraded model, toral rank conjecture, rational minimal model, semifree model, same rational homotopy type, principal holomorphic bundle, many geometrically distinct closed geodesics, whose cohomology satisfies, cochain algebra, symplectic element, trivializing open cover, closed geodesic problem, whose minimal model, rational characteristic classes, rational homotopy groups, nilpotent space, free loop space, splitting rigid, homology connection, rational homotopy types, long exact homotopy sequence, locally trivial fiber bundle, complex manifold structure Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Suppose, Proof of Theorem, Proof First, The Chas-Sullivan, Proof Denote, Proof Recall, Its Weyl, Cohomology of Lie, Proof By Proposition, Proof Note, Proof Write, Eilenberg-Mac Lane Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Lie groups and homogeneous spaces form an important family of examples of manifolds. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
shriek map, relative minimal model, bigraded model, toral rank conjecture, rational minimal model, semifree model, same rational homotopy type, principal holomorphic bundle, many geometrically distinct closed geodesics, whose cohomology satisfies, cochain algebra, symplectic element, trivializing open cover, closed geodesic problem, whose minimal model, rational characteristic classes, rational homotopy groups, nilpotent space, free loop space, splitting rigid, homology connection, rational homotopy types, long exact homotopy sequence, locally trivial fiber bundle, complex manifold structure Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Suppose, Proof of Theorem, Proof First, The Chas-Sullivan, Proof Denote, Proof Recall, Its Weyl, Cohomology of Lie, Proof By Proposition, Proof Note, Proof Write, Eilenberg-Mac Lane Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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