Examples of finite free complexes of small rank and small homology

2018/01/01 by Srikanth B. Iyengar, Mark E. Walker · 4 citations
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology

paper · pdf · doi:10.4310/acta.2018.v221.n1.a4

Abstract

This is a generalization of a topological conjecture due to Halperin; see Remark 4.8. For d 3 Conjecture 1.2 has been proved by Allday and Puppe [5, Proposition 1.1 and Corollary 1.2]; see also Walker [27, Theorem 5.3] proved it when char k =2 and H(F ) is concentrated in even degrees or in odd degrees. Corollary 4.7 below describes counterexamples when char k =2 and d 8; the DG modules constructed have cohomology in degrees 0 and 3.

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