Homotopy type through homology groups
Algebraic Topology
2025-03-14 v2
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.
Cite
@article{arxiv.2212.07509,
title = {Homotopy type through homology groups},
author = {Omar Antolín Camarena and Andrés Carnero Bravo},
journal= {arXiv preprint arXiv:2212.07509},
year = {2025}
}