The homotopy theory of function spaces: a survey

Details The homotopy theory of function spaces: a survey The homotopy theory of function spaces: a survey

2010-09-04

arxiv.org/abs/1009.0804v2

Contemp. Math. vol. 519, (2010), 3-39

Mathematics

Algebraic Topology

37 pages

Scientific paper

We survey research on the homotopy theory of the space map(X, Y) consisting of all continuous functions between two topological spaces. We summarize progress on various classification problems for the homotopy types represented by the path-components of map(X, Y). We also discuss work on the homotopy theory of the monoid of self-equivalences aut(X) and of the free loop space LX. We consider these topics in both ordinary homotopy theory as well as after localization. In the latter case, we discuss algebraic models for the localization of function spaces and their applications.

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