The index of G-transversally elliptic families in KK-theory

@article{Baldare2018TheIO,
  title={The index of G-transversally elliptic families in KK-theory},
  author={Alexandre Baldare},
  journal={arXiv: K-Theory and Homology},
  year={2018}
}
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 cup 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 Kasparov's… Expand
3 Citations

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