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Mathematics > K-Theory and Homology

arXiv:1807.11856 (math)
[Submitted on 31 Jul 2018 (v1), last revised 1 Oct 2019 (this version, v2)]

Title:Addendum to: Indefinite Kasparov modules and pseudo-Riemannian manifolds

Authors:Koen van den Dungen
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Abstract:We improve our previous results on indefinite Kasparov modules, which provide a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. In particular, we can weaken the assumptions that are imposed on indefinite Kasparov modules. Using a new theorem by Lesch and Mesland on the self-adjointness and regularity of the sum of two weakly anticommuting operators, we show that we still have an equivalence between indefinite Kasparov modules and pairs of Kasparov modules. Importantly, the weakened version of indefinite Kasparov modules now includes the main motivating example of the Dirac operator on a pseudo-Riemannian manifold. The appendix contains a construction of an approximate identity for weakly commuting operators, which is due to Lesch and Mesland.
Comments: Final version, 8 pages. This short article is an addendum to arXiv:1503.06916
Subjects: K-Theory and Homology (math.KT); Differential Geometry (math.DG)
MSC classes: 19K35, 53C50, 58B34
Cite as: arXiv:1807.11856 [math.KT]
  (or arXiv:1807.11856v2 [math.KT] for this version)
  https://doi.org/10.48550/arXiv.1807.11856
Journal reference: Annales Henri PoincarĂ©, 20 (2019), 3007-3017
Related DOI: https://doi.org/10.1007/s00023-019-00812-4

Submission history

From: Koen van den Dungen [view email]
[v1] Tue, 31 Jul 2018 15:07:29 UTC (10 KB)
[v2] Tue, 1 Oct 2019 18:31:27 UTC (10 KB)
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