The mapping class group of the Cantor tree has only geometric normal subgroups

@article{McLeay2020TheMC,
  title={The mapping class group of the Cantor tree has only geometric normal subgroups},
  author={Alan McLeay},
  journal={arXiv: Group Theory},
  year={2020}
}
  • A. McLeay
  • Published 17 February 2020
  • Mathematics
  • arXiv: Group Theory
A normal subgroup of the (extended) mapping class group of a surface is said to be geometric if its automorphism group is the mapping class group. We prove that in the case of the Cantor tree surface, every normal subgroup is geometric. We note that there is no non-trivial finite-type mapping class group for which this statement is true. We study a generalisation of the curve graph, proving that its automorphism group is again the mapping class group. This strategy is adapted from that of… 
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