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Tetrahedral Coxeter groups, large group-actions on 3-manifolds and equivariant Heegaard splittings
Zimmermann, Bruno P.
2020
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e-ISSN
2464-8728
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).
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
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale