THE GROUP OF SELF-HOMOTOPY EQUIVALENCES OF A SIMPLY CONNECTED AND 4-DIMENSIONAL CW-COMPLEX

Year 2016, Volume: 19 Issue: 19, 19 - 34, 01.06.2016

Mahmoud Benkhalifa

https://doi.org/10.24330/ieja.266190

Cited By: 2

Abstract

Let X be a CW complex, E(X) the group of homotopy classes
of self-homotopy equivalences of X and E∗(X) its subgroup of the elements
that induce the identity on homology. This paper deals with the problem 19
in [Contemp. Math., 519 (2010), 217-230]. Given a group G, find a space X
such that E(X) E∗(X) = G. For a simply connected and 4-dimensional CW-complex
X we define a group B 4 ⊂ aut(H∗(X,Z)) in term of the Whitehead exact sequence
of X and we show that this problem has a solution if G ∼= B 4 for some space X.

Keywords

Simply connected and 4-dimensional CW-complex, homotopy self-equivalences, Whitehead exact sequence, Γ-sequences, Γ-automorphisms