Artin relations in the mapping class group

  title={Artin relations in the mapping class group},
  author={Jamil Mortada},
  journal={Geometriae Dedicata},
  • Jamil Mortada
  • Published 31 July 2010
  • Mathematics
  • Geometriae Dedicata
For every integer ℓ ≥ 2, we find elements x and y in the mapping class group of an appropriate orientable surface S, satisfying the Artin relation of length ℓ. That is, xyx ... = yxy ..., where each side of the equality contains ℓ terms. By direct computations, we first find elements x and y in Mod(S) satisfying Artin relations of every even length ≥ 8, and every odd length ≥ 3. Then using the theory of Artin groups, we give two more alternative ways for finding Artin relations in Mod(S). The… 


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