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Adam Clay and Sina Zabanfahm
Automorphisms acting on the left-orderings of a bi-orderable group view print
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| Published: |
January 17, 2017 |
| Keywords: |
Orderable groups, space of orderings, automorphism group. |
| Subject: |
Primary: 20F67; Secondary: 20E36 |
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Abstract
We generalize a result of Koberda, 2011, by showing that the natural action of the automorphism group on the space of left-orderings is faithful for all nonabelian bi-orderable groups G, as well as for a certain class of left-orderable groups that includes the braid groups and mapping class groups of orientable surfaces with a single boundary component. As a corollary we show that the action of Aut(G) on ∂G is faithful whenever G is bi-orderable and hyperbolic, following the approach of Koberda. We also analyze the action of the commensurator of G on its space of virtual left-orderings.
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| Acknowledgements
Adam Clay was partially supported by NSERC grant RGPIN-2014-05465
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| Author information
Adam Clay:
Department of Mathematics, 420 Machray Hall, University of Manitoba, Winnipeg, MB, R3T 2N2
Adam.Clay@umanitoba.ca
Sina Zabanfahm:
Department of Mathematics, 420 Machray Hall, University of Manitoba, Winnipeg, MB, R3T 2N2
zabanfas@myumanitoba.ca
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