Algebraic Models in Geometry

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.

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 Université 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 Tanré 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.