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arXiv · 0805.4412

Cobordism invariance of the family index

Catarina Carvalho
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Abstract

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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Catarina Carvalho. 2009-11-06. Cobordism invariance of the family index. https://arxiv.org/abs/0805.4412

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