Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/30923
Title: Tetrahedral Coxeter groups, large group-actions on 3-manifolds and equivariant Heegaard splittings
Authors: Zimmermann, Bruno P.
Keywords: 3-manifoldfinite group-actionequivariant Heegaard splittingtetrahedrontetrahedral Coxeter group
Issue Date: 2020
Publisher: EUT Edizioni Università di Trieste
Source: Bruno P. Zimmermann, "Tetrahedral Coxeter groups, large group-actions on 3-manifolds and equivariant Heegaard splittings" in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)", EUT Edizioni Università di Trieste, Trieste, 2020
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
We consider finite group-actions on closed, orientable and nonorientable 3-manifolds M which preserve the two handlebodies of a Heegaard splitting of M of some genus g > 1 (maybe interchanging the two handlebodies). The maximal possible order of a finite group-action on a handlebody of genus g > 1 is 12(g — 1) in the orientation-preserving case and 24(g — 1) in general, and the maximal order of a finite group preserving the Heegaard surface of a Heegaard splitting of genus g is 48(g —1). This defines a hierarchy for finite group-actions on 3-manifolds which we discuss in the present paper; we present various manifolds with an action of type 48(g — 1) for small values of g, and in particular the unique hyperbolic 3-manifold with such an action of smallest possible genus g = 6 (in strong analogy with the Euclidean case of the 3-torus which has such actions for g = 3).
Type: Article
URI: http://hdl.handle.net/10077/30923
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/30923
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), 1st and 2nd Issue

Show full item record


CORE Recommender

Page view(s)

107
checked on Jun 26, 2022

Google ScholarTM

Check

Altmetric

Altmetric


This item is licensed under a Creative Commons License Creative Commons