The index of families of projective operators
Alexandre Baldare

TL;DR
This paper develops a cohomological index formula for families of projective operators on fibrations with Azumaya bundles, extending the theory of transversally elliptic operators and applying it to Dirac operators.
Contribution
It introduces a new index formula for families of projective operators using equivariant cohomology and extends the framework to projective Dirac operators.
Findings
Derived an explicit cohomological index formula in de Rham cohomology.
Computed the index of families of projective Dirac operators.
Connected the index of projective Dirac operators with transversally elliptic Dirac operators.
Abstract
Let be a central extension by an abelian finite group. In this paper, we compute the index of families of -transversally elliptic operators on a -principal bundle . We then introduce the notion of families of projective operators on fibrations equipped with an Azumaya bundle . We define and compute the index of such families using the cohomological index formula for families of -transversally elliptic operators. More precisely, a family of projective operators can be pulled back in a family of -transversally elliptic operators on the -principal bundle of trivialisations of . Through the distributional index of , we can define an index for the family of projective operators and using the index formula in equivariant cohomology for families of…
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
