
TL;DR
This paper establishes an isomorphism between two models of map space chain complexes, enabling the application of convergence theorems and reducing homotopy equivalence problems to homological algebra.
Contribution
It constructs an isomorphism between Anderson's and Arone's complexes, facilitating new applications of convergence theorems and simplifying homotopy problems.
Findings
Established an isomorphism between Anderson's and Arone's complexes
Applied Shipley's convergence theorem to Arone's model
Reduced homotopy equivalence problems to homological algebra
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
