Homologies are infinitely complex

Andras Szucs, Mark Grant

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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.
Original languageEnglish
Pages (from-to)55-62
Number of pages8
JournalTopological Methods in Nonlinear Analysis
Issue number1
Publication statusPublished - Mar 2015


  • math.AT
  • 55N10
  • primary 57R95
  • secondary 57R19
  • 57R45
  • homology of manifolds
  • realizing homology classes
  • Pontryagin-Thom construction for stratified sets
  • double-point co-oriented maps


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