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

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Abstract

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
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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