Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 39 min ago
PreprintCC BY 4.0arXiv

Morse accessibility with applications to Coxeter groups

  • Matthew Cordes
  • Annette Karrer
  • Kim Ruane
Open at sourcePDFDOICite

Abstract

In this paper we begin developing a theory of Morse hierarchies for finitely generated groups. Very roughly, a Morse hierarchy is a iterative splitting of a group over subgroups that do not contribute to the Morse boundary of the ambient group. We apply this theory to Coxeter groups, establishing new combinatorial criteria that distinguish certain Coxeter groups from other Coxeter groups as well as right-angled Artin groups up to quasi-isometry. We highlight the consequences for the right-angled case. To build the reader's intuition, the last section provides many examples of Morse hierarchies and their subtleties. Finally, there is an appendix by the second author and Vivian He that extends these ideas to the metrizable Cashen--Mackay topology on the Morse boundary.

Related

  1. The Thue-Morse substitutions and self-similar groups and algebras
    Laurent Bartholdi, José Manuel Rodríguez Caballero, Ahmed Tanbir
    Algebra and Discrete MathematicsPeer-reviewedLicence not statedFull textCombinatorics & discrete mathematicsHAL
  2. Rotation groups, mediangle graphs, and periagroups: A unified point of view on Coxeter groups and graph products of groups
    Anthony Genevois
    Groups Geometry and DynamicsPeer-reviewedCC BY13 citedGeometry & topologyOpenAlex
  3. On algebraic dynamics of birational automorphisms of Calabi-Yau manifolds and the universal Coxeter groups
    Keiji Oguiso
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Property R∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving
    Ignat Soroko
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Bounded Bruhat intervals and affine Coxeter groups
    Grant T. Barkley, Christian Gaetz
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{cordes2026morse,
  title = {{Morse accessibility with applications to Coxeter groups}},
  author = {Matthew Cordes and Annette Karrer and Kim Ruane},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05332},
  eprint = {2611.05332},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05332},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Morse accessibility with applications to Coxeter groups
AU  - Matthew Cordes
AU  - Annette Karrer
AU  - Kim Ruane
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05332
UR  - https://arxiv.org/abs/2611.05332
AB  - In this paper we begin developing a theory of Morse hierarchies for finitely generated groups. Very roughly, a Morse hierarchy is a iterative splitting of a group over subgroups that do not contribute to the Morse boundary of the ambient group. We apply this theory to Coxeter groups, establishing new combinatorial criteria that distinguish certain Coxeter groups from other Coxeter groups as well as right-angled Artin groups up to quasi-isometry. We highlight the consequences for the right-angled case. To build the reader's intuition, the last section provides many examples of Morse hierarchies and their subtleties. Finally, there is an appendix by the second author and Vivian He that extends these ideas to the metrizable Cashen--Mackay topology on the Morse boundary.
ER  -