2018/03/29 by Alexandre Baldare, Baldare, Alexandre
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1803.11148
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.