Subgroups of the group of self-homotopy equivalences

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dc.creatorArkowitz, M.
dc.creatorLupton, G.
dc.creatorMurillo, A.
dc.date2000-10-12
dc.date.accessioned2026-07-07T04:37:59Z
dc.date.available2026-07-07T04:37:59Z
dc.descriptionDenote 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.
dc.descriptionTo appear, in Contemp. Math
dc.identifierhttps://arxiv.org/abs/math/0010121
dc.identifierhttp://arxiv.org/abs/math/0010121
dc.identifierContemp. Math., Vol. 274 (2001), 21--32
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60109
dc.subjectAlgebraic Topology
dc.subject55P10; 55P62, 55Q05
dc.titleSubgroups of the group of self-homotopy equivalences
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