Cobordism invariance of the family index

Details Cobordism invariance of the family index Cobordism invariance of the family index

2008-05-28

arxiv.org/abs/0805.4412v2

Mathematics

K-Theory and Homology

20 pages, minor changes and corrections, additions in Section 4 - Corollary 4.6 is new plus discussion on Dirac operators

Scientific paper

We give a K-theory proof of the invariance under cobordism of the family index. We consider elliptic pseudodifferential families on a continuous fibre bundle with smooth fibres over a compact base space B, and define a notion of cobordant families using K^1-groups on fibrations with boundary. We show that the index of two such families is the same using properties of the push-forward map in K-theory to reduce it to families on B x R^n.

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