The index of GG-transversally elliptic families. I

  • Alexandre Baldare

    Leibniz Universität Hannover, Germany
The index of $G$-transversally elliptic families. I cover
Download PDF

A subscription is required to access this article.


We define and study the index map for families of GG-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.

Cite this article

Alexandre Baldare, The index of GG-transversally elliptic families. I. J. Noncommut. Geom. 14 (2020), no. 3, pp. 1129–1169

DOI 10.4171/JNCG/389