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.
- primary 57R95
- secondary 57R19
- homology of manifolds
- realizing homology classes
- Pontryagin-Thom construction for stratified sets
- double-point co-oriented maps