The homotopy theory of function spaces: a survey - Mathematics > Algebraic TopologyReport as inadecuate




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Abstract: We survey research on the homotopy theory of the space mapX, Y consistingof all continuous functions between two topological spaces. We summarizeprogress on various classification problems for the homotopy types representedby the path-components of mapX, Y. We also discuss work on the homotopytheory of the monoid of self-equivalences autX and of the free loop space LX.We consider these topics in both ordinary homotopy theory as well as afterlocalization. In the latter case, we discuss algebraic models for thelocalization of function spaces and their applications.



Author: Samuel Bruce Smith

Source: https://arxiv.org/







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