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PreprintarXiv licencearXiv

Regular boundary conditions and analytic K-homology

  • Alexander Engel
  • Matti Lyko
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Abstract

In their seminal work, Baum-Douglas-Taylor showed that under a certain compactness assumption, local boundary conditions for first-order elliptic operators over compact manifolds with boundary define cycles for relative K-homology. Using a systematic approach to regular boundary conditions, we generalize their result to elliptic operators of arbitrary order and to non-compact manifolds with potentially non-compact boundary. In addition, we show that under stronger regularity conditions, local boundary conditions even define cycles for absolute K-homology. In contrast to the relative classes, the resulting absolute K-homology classes are in general not independent of the choice of boundary condition.

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Cite

BibTeXRIS
BibTeX
@misc{engel2026regular,
  title = {{Regular boundary conditions and analytic K-homology}},
  author = {Alexander Engel and Matti Lyko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02899},
  eprint = {2610.02899},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02899},
}
RIS
TY  - UNPB
TI  - Regular boundary conditions and analytic K-homology
AU  - Alexander Engel
AU  - Matti Lyko
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.02899
UR  - https://arxiv.org/abs/2610.02899
AB  - In their seminal work, Baum-Douglas-Taylor showed that under a certain compactness assumption, local boundary conditions for first-order elliptic operators over compact manifolds with boundary define cycles for relative K-homology. Using a systematic approach to regular boundary conditions, we generalize their result to elliptic operators of arbitrary order and to non-compact manifolds with potentially non-compact boundary. In addition, we show that under stronger regularity conditions, local boundary conditions even define cycles for absolute K-homology. In contrast to the relative classes, the resulting absolute K-homology classes are in general not independent of the choice of boundary condition.
ER  -