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.
Citation
Mark Grant. András Szűcs. "Homologies are infinitely complex." Topol. Methods Nonlinear Anal. 45 (1) 55 - 61, 2015. https://doi.org/10.12775/TMNA.2015.003
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