Criteria for Components of a Function Space to be Homotopy Equivalent

Details Criteria for Components of a Function Space to be Homotopy Equivalent Criteria for Components of a Function Space to be Homotopy Equivalent

2006-09-22

arxiv.org/abs/math/0609650v1

Mathematics

Algebraic Topology

13 pages

Scientific paper

We give a general method that may be effectively applied to the question of whether two components of a function space have the same homotopy type. We describe certain group-like actions on function spaces. Our basic results assert that if two maps are in the same orbit under such an action, then the components of the function space that contain these maps have the same homotopy type.

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