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 |
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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: | |
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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