Affine diffeomorphism groups are undistorted

Robert Tang*

*Corresponding author for this work

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1 Citation (Scopus)


The affine diffeomorphism group (Formula presented.) of a half-translation surface (Formula presented.) comprise the self-diffeomorphisms with constant differential away from the singularities. This group coincides with the stabiliser of the associated Teichmüller disc under the action of the mapping class group on Teichmüller space. We prove that any finitely generated subgroup of (Formula presented.) is undistorted in the mapping class group. We also show that the systole map restricted to the associated electrified Nielsen core in the Teichmüller disc is a quasi-isometric embedding into the curve graph.

Original languageEnglish
Pages (from-to)747-769
Number of pages23
JournalJournal of the London Mathematical Society
Issue number2
Publication statusPublished - Sept 2021


  • 20F65
  • 30F60 (primary)
  • 57K20

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