On homotopy invariants of finite degree
We prove that homotopy invariants of finite degree distinguish homotopy classes of maps of a connected compact CW-complex to a nilpotent connected CW-complex with finitely generated homotopy groups.
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arXiv subjects
Semen Podkorytov
Publications and source records attributed to Semen Podkorytov.
On homology of map spaces
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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