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Relative K-homology of higher-order differential operators

Fries, Magnus LU orcid (2025) In Journal of Functional Analysis 288(1).
Abstract

We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order relative spectral triple gives rise to a relative K-homology cycle. In the case of an elliptic differential operator on a compact smooth manifold with boundary, we calculate the K-homology boundary map of the constructed relative K-homology cycle to obtain a generalization of the Baum-Douglas-Taylor index theorem.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Boundary value problems, Differential operators, K-homology, Spectral triples
in
Journal of Functional Analysis
volume
288
issue
1
article number
110678
publisher
Academic Press
external identifiers
  • scopus:85204186814
ISSN
0022-1236
DOI
10.1016/j.jfa.2024.110678
language
English
LU publication?
yes
id
7d01944f-f68a-45f7-8043-aed18fa74cde
date added to LUP
2024-11-12 17:26:37
date last changed
2025-04-04 13:59:13
@article{7d01944f-f68a-45f7-8043-aed18fa74cde,
  abstract     = {{<p>We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order relative spectral triple gives rise to a relative K-homology cycle. In the case of an elliptic differential operator on a compact smooth manifold with boundary, we calculate the K-homology boundary map of the constructed relative K-homology cycle to obtain a generalization of the Baum-Douglas-Taylor index theorem.</p>}},
  author       = {{Fries, Magnus}},
  issn         = {{0022-1236}},
  keywords     = {{Boundary value problems; Differential operators; K-homology; Spectral triples}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Functional Analysis}},
  title        = {{Relative K-homology of higher-order differential operators}},
  url          = {{http://dx.doi.org/10.1016/j.jfa.2024.110678}},
  doi          = {{10.1016/j.jfa.2024.110678}},
  volume       = {{288}},
  year         = {{2025}},
}