On the group of self-homotopy equivalences of a 2-connected and 6-dimensional CW-complex

2022/10/19 by Benkhalifa, Mahmoud
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.10704

Abstract

Let X be a \text\rm2-connected and \text\rm6-dimensional CW-complex X such that H₃(X)⊗\Z₂=0. This paper aims to describe the group \E(X) of the self-homotopy equivalences of X modulo its normal subgroup \E_*(X) of the elements that induce the identity on the homology groups. Making use of the Whitehead exact sequence of X, denoted by WES(X), we define the group ΓS(X) of Γ-automorphisms of WES(X) and we prove that \E(X)/\E_*(X)≅ ΓS(X).

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