Homotopy type through homology groups
arXiv:2212.07509 · doi:10.1007/s40590-024-00605-8
Abstract
We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive dimensions. We also show other pairs of dimensions for which the last result can be generalized.