2013/12/31 by Denis Perrot, Perrot, Denis · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT
paper · pdf · doi:10.48550/arxiv.1401.0225
40 pages, sections 6-8 have been removed and will be included in a new preprint
openalex publication_date 2013/12/31 · arxiv created 2016/12/08 · arxiv updated 2016/12/09 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We develop a local index theory for Fourier-integral operators associated to non-proper and non-isometric actions of Lie groupoids on smooth submersions. To such action is associated a short exact sequence of algebras, relating genuine Fourier-integral operators to their non-commutative symbol. We then compute the connecting map induced by this extension on periodic cyclic cohomology. When cyclic cohomology is localized at appropriate isotropic submanifolds of the groupoid in question, we find that the connecting map is expressed in terms of an explicit Wodzicki-type residue formula, which involves the jets of non-commutative symbols at the fixed-point set of the action.