The group of self-homotopy equivalences of A n 2 A _n ²-polyhedra

Abstract

Let X be a finite type A2n-polyhedron, n≥2. In this paper, we study the quotient group E(X)/E∗(X), where E(X) is the group of self-homotopy equivalences of X and E∗(X) the subgroup of self-homotopy equivalences inducing the identity on the homology groups of X. We show that not every group can be realised as E(X) or E(X)/E∗(X) for X an A2n-polyhedron, n≥3, and specific results are obtained for n=2.

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