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Mathematics > K-Theory and Homology

arXiv:2411.01646 (math)
[Submitted on 3 Nov 2024 (v1), last revised 6 Nov 2024 (this version, v2)]

Title:Coronas and Callias type operators in coarse geometry

Authors:Ulrich Bunke, Matthias Ludewig
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Abstract:We interpret the coarse symbol and index class of a Callias type Dirac operator $D+\Psi$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$ itself determined by $\Psi$. Local positivity of $D$ and local invertibility of $\Psi$ are incorporated in terms of support conditions on the $K$-theoretic level.
Comments: 106 pages
Subjects: K-Theory and Homology (math.KT); Algebraic Topology (math.AT); Differential Geometry (math.DG); Operator Algebras (math.OA)
Cite as: arXiv:2411.01646 [math.KT]
  (or arXiv:2411.01646v2 [math.KT] for this version)
  https://doi.org/10.48550/arXiv.2411.01646

Submission history

From: Matthias Ludewig [view email]
[v1] Sun, 3 Nov 2024 17:52:20 UTC (97 KB)
[v2] Wed, 6 Nov 2024 12:15:58 UTC (97 KB)
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