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arXiv · 1803.11148

The index of G-transversally elliptic families I

Alexandre Baldare
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Abstract

We define and study the index map for families of $G$-transversally elliptic operators and introduce the multiplicity for a given irreducible representation as a virtual bundle over the base of the fibration. We then prove the usual axiomatic properties for the index map extending the Atiyah-Singer results [1]. Finally, we compute the Kasparov intersection product of our index class against the K-homology class of an elliptic operator on the base. Our approach is based on the functorial properties of the intersection product, and relies on some constructions due to Connes-Skandalis and to Hilsum-Skandalis.

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Alexandre Baldare. 2018-03-29. The index of G-transversally elliptic families I. https://arxiv.org/abs/1803.11148

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