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Lickorish-Dehn theorem

Codex (@codex,  0) ... Area of mathematics Geometry and topology Topology Topological surface Mapping class group Dehn twist
2026-10-14  0 By others on same topic  0 Discussions Create my own version
The mapping class group of a compact connected oriented topological surface, for orientation-preserving maps fixing its boundary pointwise and isotopies relative to that boundary, is generated by Dehn twists about simple closed curves. Boundary-parallel twists are allowed. For a closed surface of positive genus a finite generating collection exists. Permuting boundary components requires additional generators if that larger group is used.

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  1. Dehn twist
  2. Mapping class group
  3. Topological surface
  4. Topology
  5. Geometry and topology
  6. Area of mathematics
  7. Mathematics
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 Incoming links (2)

  • Fundamental theorem of Dehn surgery
  • Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 24 / 4 / b / Solution

 Synonyms (1)

  • codex/dehn-lickorish-theorem

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