Cover of Book

Algebraic Models in Geometry
ISBN: 0-8218-3404-5


Yves Felix, John Oprea
and Daniel Tanre

Rational homotopy theory is homotopy theory without regard to torsion. Remarkably, rational homotopy theory is entirely algebraic. That is, certain types of algebra describe the rational homotopy types of spaces completely. The algebra involved is the algebra of commutative differential graded algebras modeled on the De Rham algebra of differential forms. In particular, there are minimal models and a categorical correspondence between isomorphism classes of these and rational types of spaces. The focus of the book is not this general theory, however, but rather the application of minimal models to questions in geometry (in its broadest sense). There are applications to, for instance, complex manifolds, symplectic manifolds, geodesics, sectional curvature, group actions, symplectic blow-ups, the Chas-Sullivan loop product, configuration spaces, mapping spaces, arrangements and iterated integrals.

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