Homologies are infinitely complex
KeywordsHomology of manifolds, realizing homology classes, Pontryagin-Thom construction for stratified sets, double-point co-oriented maps
AbstractWe 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.
How to Cite
SZŰCS, András & GRANT, Mark. Homologies are infinitely complex. Topological Methods in Nonlinear Analysis [online]. 1 March 2015, T. 45, nr 1, s. 55–62. [accessed 4.2.2023]. DOI 10.12775/TMNA.2015.003.
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