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PreprintCC BY 4.0arXiv

Triviality of K-homology classes of Euler characteristic operators of stratified pseudomanifolds

  • Mohammadali Aligholi
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Abstract

We show that the K-homology classes of the Euler characteristic operators associated with the minimal and maximal ideal boundary conditions of the de Rham differential on the regular part of a connected compact Thom-Mather stratified pseudomanifold, equipped with an adapted metric, are trivial beyond their indices. These indices are the Euler characteristics of the corresponding L2-cohomologies. This generalizes a result of J. Rosenberg for manifolds. The proof uses Witten deformation of the de Rham operator associated with a stratified Morse function, following the work of Álvarez López and Calaza.

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Cite

BibTeXRIS
BibTeX
@misc{aligholi2026triviality,
  title = {{Triviality of $K$-homology classes of Euler characteristic operators of stratified pseudomanifolds}},
  author = {Mohammadali Aligholi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27476},
  eprint = {2610.27476},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27476},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Triviality of K-homology classes of Euler characteristic operators of stratified pseudomanifolds
AU  - Mohammadali Aligholi
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27476
UR  - https://arxiv.org/abs/2610.27476
AB  - We show that the K-homology classes of the Euler characteristic operators associated with the minimal and maximal ideal boundary conditions of the de Rham differential on the regular part of a connected compact Thom-Mather stratified pseudomanifold, equipped with an adapted metric, are trivial beyond their indices. These indices are the Euler characteristics of the corresponding L^2-cohomologies. This generalizes a result of J. Rosenberg for manifolds. The proof uses Witten deformation of the de Rham operator associated with a stratified Morse function, following the work of Álvarez López and Calaza.
ER  -