On homotopy invariants of finite degree
Semen Podkorytov
TL;DR
This paper demonstrates that homotopy invariants of finite degree can uniquely identify homotopy classes of maps between certain types of CW-complexes, specifically from connected compact to nilpotent connected CW-complexes with finitely generated homotopy groups.
Contribution
It establishes that finite degree homotopy invariants are sufficient to distinguish homotopy classes in a broad class of CW-complexes, extending understanding of homotopy invariants.
Findings
Homotopy invariants of finite degree distinguish homotopy classes.
Applicable to maps from connected compact to nilpotent CW-complexes.
Results hold for complexes with finitely generated homotopy groups.
Abstract
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis