Bordism of regularly defective maps

Bechtluft-Sachs, Stefan (2003) Bordism of regularly defective maps. Mathematische Zeitschrift, 245. pp. 529-543.

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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 [17] 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.

Item Type: Article
Keywords: Bordism of regularly defective maps;
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1588
Depositing User: Stefan Bechtluft-Sachs
Date Deposited: 16 Oct 2009 09:49
Journal or Publication Title: Mathematische Zeitschrift
Publisher: Springer Verlag
Refereed: Yes

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