Homologies are infinitely complex

DOI10.12775/TMNA.2015.003zbMATH Open1368.57013arXiv1309.1445OpenAlexW2964159225MaRDI QIDQ519434

András Szűcs, Mark Grant

Publication date: 4 April 2017

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1309.1445

zbMATH Keywords

double point co-oriented mapsrealizing homology classesstratified sets

Mathematics Subject Classification ID

Singular homology and cohomology theory (55N10) Algebraic topology on manifolds and differential topology (57R19) Realizing cycles by submanifolds (57R95)

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