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Mathematics > K-Theory and Homology

arXiv:2210.02332 (math)
[Submitted on 5 Oct 2022 (v1), last revised 26 May 2024 (this version, v3)]

Title:K-theory and index theory on manifolds with a proper Lie group action

Authors:Gennadi Kasparov
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Abstract:The paper is devoted to the index theory of orbital and transverse elliptic operators on manifolds with a proper Lie group action. It corrects errors of my previous paper (published in JNCG in 2016) on transverse operators and contains new results. The two index theories, orbital and transverse, are very much intertwined and interdependent, and are treated together. The theory of orbital operators is developed from the basic definitions to the final index theorem. The KK-theoretic proofs of index theorems for elliptic, t-elliptic and orbital elliptic operators are given in sections 9, 10, 11. Throughout the paper, we use a simpler method in constructing pseudo-differential operators.
Comments: 52 pages
Subjects: K-Theory and Homology (math.KT)
Cite as: arXiv:2210.02332 [math.KT]
  (or arXiv:2210.02332v3 [math.KT] for this version)
  https://doi.org/10.48550/arXiv.2210.02332

Submission history

From: Gennadi Kasparov [view email]
[v1] Wed, 5 Oct 2022 15:36:41 UTC (50 KB)
[v2] Wed, 31 May 2023 00:19:27 UTC (51 KB)
[v3] Sun, 26 May 2024 15:27:00 UTC (45 KB)
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