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

Authors : Mahmoud Benkhalifa

Pages : 19-34

Doi:10.24330/ieja.266190

View : 17 | Download : 12

Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :Let X be a CW complex, Einsert ignore into journalissuearticles values(X); the group of homotopy classes of self-homotopy equivalences of X and E∗insert ignore into journalissuearticles values(X); its subgroup of the elements that induce the identity on homology. This paper deals with the problem 19 in [Contemp. Math., 519 insert ignore into journalissuearticles values(2010);, 217-230]. Given a group G, find a space X such that Einsert ignore into journalissuearticles values(X); E∗insert ignore into journalissuearticles values(X); = G. For a simply connected and 4-dimensional CW-complex X we define a group B 4 ⊂ autinsert ignore into journalissuearticles values(H∗insert ignore into journalissuearticles values(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