(Un)distorted stabilisers in the handlebody group

We study geometric properties of stabilisers in the handlebody group. We find that stabilisers of meridians are undistorted, while stabilisers of primitive curves or annuli are exponentially distorted for large enough genus.

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Bibliographic Details
Published in:Journal of topology 2021-06, Vol.14 (2), p.460-487
Main Author: Hensel, Sebastian
Format: Article
Language:English
Subjects:
20F65
57M07 (primary)
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Description
Summary:We study geometric properties of stabilisers in the handlebody group. We find that stabilisers of meridians are undistorted, while stabilisers of primitive curves or annuli are exponentially distorted for large enough genus.
ISSN:1753-8416
1753-8424
DOI:10.1112/topo.12186