Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 33 min ago
PreprintarXiv licencearXiv

Selflessness, MIF and opposition in groups acting on exotic buildings

  • Corentin Le Bars
  • Elyasheev Leibtag
  • Itamar Vigdorovich
Open at sourcePDFDOICite

Abstract

We prove that groups acting freely and cocompactly on (possibly exotic) affine buildings of type Ã2 and C̃2 are mixed-identity free and have selfless reduced C*-algebras. These results follow from a strong form of ping-pong dynamics that we call 'transversal contractivity'. Our main geometric result regards domesticity properties of elements in the associated polygons at infinity: we prove that, in our context, the opposite geometry of a hyperbolic element is topologically large.

Related

  1. C*-selflessness of groups of homeomorphisms
    Ryoya Arimoto
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  2. Selflessness for twisted group C*-algebras of amenable groups and their inclusions
    Tron Omland
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  3. Finite Cyclic Fundamental Groups and Exotic Universal Covers from the Cartwright--Steger Surface
    Anar Akhmedov, B. Doug Park, Sümeyra Sakallı +1
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  4. Large Ree groups acting point and line-primitively on finite generalised quadrangles
    Vishnuram Arumugam
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Drift and joint minimal displacement for groups acting on hyperbolic spaces
    Koji Fujiwara, Ryokichi Tanaka
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{bars2026selflessness,
  title = {{Selflessness, MIF and opposition in groups acting on exotic buildings}},
  author = {Corentin Le Bars and Elyasheev Leibtag and Itamar Vigdorovich},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17129},
  eprint = {2609.17129},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17129},
}
RIS
TY  - UNPB
TI  - Selflessness, MIF and opposition in groups acting on exotic buildings
AU  - Corentin Le Bars
AU  - Elyasheev Leibtag
AU  - Itamar Vigdorovich
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17129
UR  - https://arxiv.org/abs/2609.17129
AB  - We prove that groups acting freely and cocompactly on (possibly exotic) affine buildings of type Ã_2 and C̃_2 are mixed-identity free and have selfless reduced C^*-algebras. These results follow from a strong form of ping-pong dynamics that we call 'transversal contractivity'. Our main geometric result regards domesticity properties of elements in the associated polygons at infinity: we prove that, in our context, the opposite geometry of a hyperbolic element is topologically large.
ER  -