Homotopy theory of infinite dimensional manifolds

Abstract

In the past several years there has been considerable interest in the theory of infinite dimensional differentiable manifolds. While most of the developments have quite properly stressed the differentiable structure, it is nevertheless true that the results and techniques are in large part homotopy theoretic in nature. By and large homotopy theoretic results have been brought in on an ad hoc basis in the proper degree of generality appropriate for the application immediately at hand. The result has been a number of overlapping lemmas of greater or lesser generality scattered through the published and unpublished literature. The present paper grew out of the author's belief that it would serve a useful purpose to collect some of these results and prove them in as general a setting as is presently possible.