Homologies are infinitely complex
Algebraic Topology
2014-03-07 v2
Abstract
We show that for any k>1, stratified sets of finite complexity are insufficient to realize all homology classes of codimension k in all smooth manifolds. We also prove a similar result concerning smooth generic maps whose double-point sets are co-oriented.
Keywords
Cite
@article{arxiv.1309.1445,
title = {Homologies are infinitely complex},
author = {Mark Grant and Andras Szucs},
journal= {arXiv preprint arXiv:1309.1445},
year = {2014}
}
Comments
5 pages; v2: Very minor corrections, to appear in Topol. Methods Nonlinear Anal