## Rational Homotopy Theory

Rational homotopy theory is analogous to the study of linear algebra
versus general ring and module theory. On the one hand, it is simpler,
but yet has useful applications and predictive power. It isolates in
algebraic topology those questions and techniques that deal with
non-torsion data.

For example, if M is an orientable manifold, using the differentiable
forms, one can calculate the real cohomology of M. Quillen and Sullivan
realized 30 years ago that this was just the top level of information
available-- in fact, information about the entire homotopy type of
M is implicit in these differentiable forms. This, along with related
methods of localization and completions, marked a change in the
approach to the sudy of homotopy types of topological spaces.

The rational homotopy type of a space X provides the backbone, to which
more detailed information concerning various primes is attached to
build a picture of the homotopy type of X. The techniques involved in
studying rational homotopy theory are simpler and more algebraic
than those needed in traditional algebraic topology.

This course should be of use to students studying topology, commutative
algebra, geometry, and several complex variables. The book by
Halperin, et al provides an overall survey of the area.

@book {MR2002d:55014,

AUTHOR = {F{\'e}lix, Yves and Halperin, Stephen and Thomas, Jean-Claude},

TITLE = {Rational homotopy theory},

SERIES = {Graduate Texts in Mathematics},

VOLUME = {205},

PUBLISHER = {Springer-Verlag},

ADDRESS = {New York},

YEAR = {2001},

PAGES = {xxxiv+535},

ISBN = {0-387-95068-0},

MRCLASS = {55P62 (18Gxx 55U35)},

MRNUMBER = {2002d:55014},

MRREVIEWER = {John F. Oprea},

}