Skip to content
DraconiticResearch
Search Sources API
181,686 studies31 sourcesUpdated 2 min ago
PreprintarXiv licencearXiv

Recognizing convergence actions as proper isometric actions on hyperbolic spaces

  • Lihuang Ding
  • Abdul Zalloum
Open at sourcePDFDOICite

Abstract

Relying merely on B.I. (a.k.a. Bowditch's intelligence), we show that whenever a group G admits a convergence action on a compact perfect metrizable space M, there is a hyperbolic space X along with a proper isometric action of G on X inducing a G-equivariant homeomorphism f:M → ∂ X. This answers a question by Misha Kapovich.

Related

  1. Warped cones associated to isometric free actions do not have geometric property (T)
    Ryo Toyota
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  2. Isometric Embeddings of Asymptotically Hyperbolic Manifolds into Hyperbolic Space
    Marco Usula
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. II
    Kai Mao
    HALPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryAnalysis & PDEsHALarXiv
  4. Positive sectional curvature and non-isometric circle actions on a family of eleven-spheres
    Shaoqiang Deng, Zhiguang Hu, Hui Zhang
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  5. Roe algebras and coarse index maps for spaces with proper actions of étale groupoids. I
    Kai Mao
    HALPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryAnalysis & PDEsHALarXiv

Cite

BibTeXRIS
BibTeX
@misc{ding2026recognizing,
  title = {{Recognizing convergence actions as proper isometric actions on hyperbolic spaces}},
  author = {Lihuang Ding and Abdul Zalloum},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36211},
  eprint = {2610.36211},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36211},
}
RIS
TY  - UNPB
TI  - Recognizing convergence actions as proper isometric actions on hyperbolic spaces
AU  - Lihuang Ding
AU  - Abdul Zalloum
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36211
UR  - https://arxiv.org/abs/2610.36211
AB  - Relying merely on B.I. (a.k.a. Bowditch's intelligence), we show that whenever a group G admits a convergence action on a compact perfect metrizable space M, there is a hyperbolic space X along with a proper isometric action of G on X inducing a G-equivariant homeomorphism f:M → ∂ X. This answers a question by Misha Kapovich.
ER  -