A criterion for the existence of periodic points based on the eigenvalues of maps induced in cohomology

2019/08/29 by Michalina Horecka, Paweł Raźny, Horecka, Michalina +1
Mathematics · #37C25 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1908.11109

openalex publication_date 2019/08/29 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We present a criterion for the existence of periodic points based on the eigenvalues of maps induced in cohomology for spaces with rational cohomology isomorphic to a tensor product of a graded exterior algebra with generators in odd dimensions and a graded algebra with all elements of even degree. We give a number of natural examples of such spaces and provide some non-trivial ones. We also give a counterexample to a claim in \citeduan given there without proof.

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