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Nullhomotopic equivariant shifts and Borsuk-Ulam-compatible compact abelian groups

  • Alexandru Chirvasitu
  • Alexander Dąbrowski
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Abstract

We disprove the classical version of the Borsuk-Ulam-flavored conjecture, due to Baum-D{ą}browski-Hajac, that free actions X× 𝔾→ X on non-empty compact Hausdorff spaces by non-trivial compact groups admit no equivariant maps X*𝔾→ X. Specifically, among non-trivial compact abelian 𝔾, the conjecture fails precisely when 𝔾 is torsion-free profinite.

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Cite

BibTeXRIS
BibTeX
@misc{chirvasitu2026nullhomotopic,
  title = {{Nullhomotopic equivariant shifts and Borsuk-Ulam-compatible compact abelian groups}},
  author = {Alexandru Chirvasitu and Alexander Dąbrowski},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10111},
  eprint = {2610.10111},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10111},
}
RIS
TY  - UNPB
TI  - Nullhomotopic equivariant shifts and Borsuk-Ulam-compatible compact abelian groups
AU  - Alexandru Chirvasitu
AU  - Alexander Dąbrowski
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.10111
UR  - https://arxiv.org/abs/2610.10111
AB  - We disprove the classical version of the Borsuk-Ulam-flavored conjecture, due to Baum-D{ą}browski-Hajac, that free actions X× 𝔾→ X on non-empty compact Hausdorff spaces by non-trivial compact groups admit no equivariant maps X*𝔾→ X. Specifically, among non-trivial compact abelian 𝔾, the conjecture fails precisely when 𝔾 is torsion-free profinite.
ER  -