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Presentation
Subgroups of the Mapping Class Group Corresponding to 1-Dimensional Strata in the Branch Locus of Moduli Space
Joint Mathematics Meetings (2017)
  • Sean A Broughton
Abstract
The branch locus B_s in M_s, the moduli space of surfaces of genus s, is the
subspace of surfaces with a non-trivial automorphism group. The branch locus
admits a strati fication by finitely many, irreducible, complex algebraic varieties,
corresponding to surfaces whose automorphism groups have topologically
equivalent actions. In turn, each stratum determines a conjugacy classes of fi nite sub-
groups of the mapping class of genus : The correspondence between strata and
conjugacy classes of nite subgroups is not 1-1, but is fairly close to 1-1. The
strata of dimension 0 correspond to quasi-platonic surfaces, which are very well
studied. In this talk we take the next step and study the subgroups corresponding
to strata of dimension 1, where the quotient surface S/Aut(S) is either is a sphere
with four branch points or a torus with one branch point. We discuss the topology
of these strata in terms of the structure of the group.
Keywords
  • Riemann surface,
  • moduli space,
  • branch locus,
  • mapping class group
Publication Date
January 6, 2017
Location
Atlanta, GA
Citation Information
Sean A Broughton. "Subgroups of the Mapping Class Group Corresponding to 1-Dimensional Strata in the Branch Locus of Moduli Space" Joint Mathematics Meetings (2017)
Available at: http://works.bepress.com/allen_broughton/53/
Creative Commons License
Creative Commons License
This work is licensed under a Creative Commons CC_BY-NC-SA International License.