2000/10/12 by M. Arkowitz, G. Lupton, A. Murillo
Mathematics · #math.AT #msc:55P10 #msc:55P62 #msc:55Q05
published as Contemp. Math., Vol. 274 (2001), 21--32 · To appear, in Contemp. Math
arxiv created 2000/10/12 · arxiv updated 2009/11/30
Denote by E(Y) the group of homotopy classes of self-homotopy equivalences of a finite-dimensional complex Y. We give a selection of results about certain subgroups of E(Y). We establish a connection between the Gottlieb groups of Y and the subgroup of E(Y) consisting of homotopy classes of self-homotopy equivalences that fix homotopy groups through the dimension of Y, denoted by E_#(Y). We give an upper bound for the solvability class of E_#(Y) in terms of a cone decomposition of Y. We dualize the latter result to obtain an upper bound for the solvability class of the subgroup of E(Y) consisting of homotopy classes of self-homotopy equivalences that fix cohomology groups with various coefficients. We also show that with integer coefficients, the latter group is nilpotent.