Bordism of regularly defective maps
Bechtluft-Sachs, Stefan (2003) Bordism of regularly defective maps. Mathematische Zeitschrift, 245 . pp. 529-543.
To a topological space V we assign the bordism group Ndef n (V ) of reg- ularly defective maps f : M◦→V on closed n-dimensional manifolds M. These are triples (M,, f) where is a closed submanifold ⊂ M and f a continuous map f : M r → V . We briefly review the construction of the defect complex DV given by M. Rost in  and show that Ndef n (V ) is isomorphic to ordinary bordism Nn(DV ). The bordism classes in Ndef n (V ) ∼= Nn(DV ) are detected by characteristic numbers twisted with cohomology classes of DV . Some of these numbers can be described without reference to the defect complex. As an example we treat the case of the circle V = S1. We compute Ndef n (S1), construct a basis and a complete set of characteristic numbers.
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