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Criteria for Components of a Function Space to be Homotopy Equivalent

Gregory Lupton·Samuel Bruce Smith
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Abstract

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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Gregory Lupton, Samuel Bruce Smith. 2006-09-22. Criteria for Components of a Function Space to be Homotopy Equivalent. https://arxiv.org/abs/math/0609650

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