On the Lusternik-Schnirelmann category of spaces with 2-dimensional fundamental group

2007/09/25 by Alexander Dranishnikov, Dranishnikov, A.
Mathematics · #55M30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0709.4018

openalex publication_date 2007/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The following inequality \cat X≤ \cat Y+\lceil(hd(X)-r)/(r+1)\rceil holds for every locally trivial fibration between ANE spaces f:X→ Y which admits a section and has the r-connected fiber where hd(X) is the homotopical dimension of X. We apply this inequality to prove that \cat X≤ \lceil(dim X-1)/(2)\rceil+cd(π₁(X)) for every complex X with cd(π₁(X))≤ 2.

Citations

• Small values of Lusternik-Schnirelmann and systolic categories for manifolds

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