Homologies are infinitely complex
classification
🧮 math.AT
keywords
setssmoothclassesco-orientedcodimensioncomplexcomplexityconcerning
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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.
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