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(Un)distorted stabilisers in the handlebody group

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 Added by Sebastian Hensel
 Publication date 2019
  fields
and research's language is English




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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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We construct examples of fibered three-manifolds with first Betti number at least 2 and with fibered faces all of whose monodromies extend to a handlebody.
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