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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