On homology of map spaces

Published 8 Feb 2011 in math.AT | (1102.1645v1)

Abstract: Following an idea of Bendersky-Gitler, we construct an isomorphism between Anderson's and Arone's complexes modelling the chain complex of a map space. This allows us to apply Shipley's convergence theorem to Arone's model. As a corollary, we reduce the problem of homotopy equivalence for certain "toy" spaces to a problem in homological algebra.

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Semen Podkorytov

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