WHEN HOMOLOGY EQUIVALENCE IMPLIES HOMOTOPY EQUIVALENCE FOR 2-COMPLEXES

[摘要] Let K and L be two finite 2-dimensional CW-complexes with the same fundamental group. If the fundamental group is finite and abelian, it is well known that K and L are homotopy equivalent and simple homotopy equivalent if and only if they are homology equivalent via a map that induces an isomorphism on the fundamental group. We generalize this result to left-iterated semi-direct products of finite cyclic groups. We must add other hypotheses which were automatically satisfied in the abelian case. Example of groups that satisfy the hypotheses include dihedral groups of order 4n.

[发布日期] 1991-12-16