Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 48 min ago
PreprintarXiv licencearXiv

Nonarchimedean discrete groups and quasi-isometric doubles of free groups

  • Konstantinos Tsouvalas
Open at sourcePDFDOICite

Abstract

For any nonarchimedean local field k, we exhibit the first examples of Zariski-dense, discrete subgroups of special linear groups over k, which are not commensurable to any lattice in the points of a semisimple group over a local field, and contain an infinite index subgroup isomorphic to a lattice in the k-points of a higher rank k-semisimple group. We prove that any Gromov-hyperbolic double of a non-elementary free group along a cyclic subgroup embeds as a quasi-isometrically embedded subgroup of SL5(k')× SL5(k'), where k' is a discretely valued field. More precisely, k' is the field of rational functions k(t) equipped with the Gauss valuation and k is any nonarchimedean local field of characteristic not equal to $2$ or $3$.

Related

  1. Discrete intermediate dimensions: endpoints, spectra and quasi-isometric invariance
    Jinjun Li, Lifeng Xi, Shuqin Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Proliferation Transitions for Quantum Doubles of Groups
    Yuhan Gai, Sakura Schafer-Nameki
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCondensed matterarXiv
  3. Non-maximal quasi-isometric PU2,n+1-representations via alternating surfaces in complex pseudo-hyperbolic spaces
    Qiongling Li, Junming Zhang
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. The Structure of a Non-Isometric Non-Contractive Bijection of a Hereditarily Precompact Quasi-Metric Space
    Thomas Duzer
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv
  5. Explicit quasi-periodic solutions to the discrete derivative nonlinear Schrödinger equation
    Xiaoxue Xu, Wei Liu, Junyi Zhu
    arXivPreprintarXiv licenceFull textMathematical physicsStatistical & nonlinear physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{tsouvalas2026nonarchimedean,
  title = {{Nonarchimedean discrete groups and quasi-isometric doubles of free groups}},
  author = {Konstantinos Tsouvalas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16291},
  eprint = {2610.16291},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16291},
}
RIS
TY  - UNPB
TI  - Nonarchimedean discrete groups and quasi-isometric doubles of free groups
AU  - Konstantinos Tsouvalas
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16291
UR  - https://arxiv.org/abs/2610.16291
AB  - For any nonarchimedean local field k, we exhibit the first examples of Zariski-dense, discrete subgroups of special linear groups over k, which are not commensurable to any lattice in the points of a semisimple group over a local field, and contain an infinite index subgroup isomorphic to a lattice in the k-points of a higher rank k-semisimple group. We prove that any Gromov-hyperbolic double of a non-elementary free group along a cyclic subgroup embeds as a quasi-isometrically embedded subgroup of SL_5(k')× SL_5(k'), where k' is a discretely valued field. More precisely, k' is the field of rational functions k(t) equipped with the Gauss valuation and k is any nonarchimedean local field of characteristic not equal to $2$ or $3$.
ER  -