The index of leafwise G-transversally elliptic operators on foliations

@article{Baldare2020TheIO,
  title={The index of leafwise G-transversally elliptic operators on foliations},
  author={Alexandre Baldare and Moulay-Tahar Benameur},
  journal={arXiv: K-Theory and Homology},
  year={2020}
}
We introduce and study the index morphism for G-invariant leafwise G-transversally elliptic operators on smooth closed foliated manifolds which are endowed with leafwise actions of the compact group G. We prove the usual axioms of excision, multiplicativity and induction for closed subgroups. In the case of free actions, we relate our index class with the Connes-Skandalis index class of the corresponding leafwise elliptic operator on the quotient foliation. Finally we prove the compatibility of… Expand
2 Citations

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