Reflection length at infinity in hyperbolic reflection groups

• Verfasst von: Lotz, Marco [VerfasserIn]
• Titel: Reflection length at infinity in hyperbolic reflection groups
• Verf.angabe: Marco Lotz
• E-Jahr: 2024
• Jahr: 26. Juli 2024
• Umfang: 23 S.
• Illustrationen: Illustrationen
• Fussnoten: Gesehen am 28.11.2024
• Titel Quelle: Enthalten in: Expert review of medical devices
• Ort Quelle: Abingdon : Taylor & Francis Group, 2004
• Jahr Quelle: 2024
• Band/Heft Quelle: (2024), ahead of print, Seite 1-23
• ISSN Quelle: 1745-2422
• DOI: doi:10.1515/jgth-2023-0073
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1909865885

Abstract

In a discrete group generated by hyperplane reflections in the ????-dimensional hyperbolic space, the reflection length of an element is the minimal number of hyperplane reflections in the group that suffices to factor the element. For a Coxeter group that arises in this way and does not split into a direct product of spherical and affine reflection groups, the reflection length is unbounded. The action of the Coxeter group induces a tessellation of the hyperbolic space. After fixing a fundamental domain, there exists a bijection between the tiles and the group elements. We describe certain points in the visual boundary of the ????-dimensional hyperbolic space for which every neighbourhood contains tiles of every reflection length. To prove this, we show that two disjoint hyperplanes in the ????-dimensional hyperbolic space without common boundary points have a unique common perpendicular.