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PreprintarXiv licencearXiv

Homotopies of constant Cuntz classes in pure C*-algebras

  • Chrisil Ouseph
  • Andrew S. Toms
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Abstract

Let A be a unital, simple, separable, and pure C*-algebra. We prove that, for every a∈ A+, the set of positive elements in A having the same Cuntz class as a is path-connected. This may be viewed as a generalization to positive elements of the classical homotopy theory of projection classes and extends a line of results on the topology of constant Cuntz classes that previously required stronger regularity hypotheses to the class of pure C*-algebras, which notably contains all selfless algebras.

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Cite

BibTeXRIS
BibTeX
@misc{ouseph2026homotopies,
  title = {{Homotopies of constant Cuntz classes in pure $C^*$-algebras}},
  author = {Chrisil Ouseph and Andrew S. Toms},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12219},
  eprint = {2610.12219},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12219},
}
RIS
TY  - UNPB
TI  - Homotopies of constant Cuntz classes in pure C^*-algebras
AU  - Chrisil Ouseph
AU  - Andrew S. Toms
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12219
UR  - https://arxiv.org/abs/2610.12219
AB  - Let A be a unital, simple, separable, and pure C^*-algebra. We prove that, for every a∈ A_+, the set of positive elements in A having the same Cuntz class as a is path-connected. This may be viewed as a generalization to positive elements of the classical homotopy theory of projection classes and extends a line of results on the topology of constant Cuntz classes that previously required stronger regularity hypotheses to the class of pure C^*-algebras, which notably contains all selfless algebras.
ER  -