• Corpus ID: 239885526

Notes on hyperelliptic mapping class groups

  title={Notes on hyperelliptic mapping class groups},
  author={Marco Boggi},
  • M. Boggi
  • Published 26 October 2021
  • Mathematics
Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural epimorphisms between mapping class groups of surfaces with marked points. We study these groups in a systematic way. An application of this theory is a counterexample to the genus 2 case of a conjecture by Putman and Wieland on virtual linear representations of mapping… 


Point pushing, homology, and the hyperelliptic involution
The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at $$t=-1$$t=-1
We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The
Linear Representations of Hyperelliptic Mapping Class Groups
Let $p:S\to S_g$ be a finite $G$-covering of a closed surface of genus $g\geq 1$ and let $B$ its branch locus. To this data, it is associated a representation of a finite index subgroup of the
Discrete Groups and Geometry: Moduli of Riemann surfaces with symmetry
The moduli space A1. 9 of Riemann surfaces with genus 9 > 2 contains an important subset corresponding to surfaces admitting non-trivial automorphisms. In this paper, we study certain irreducible
A primer on mapping class groups
Given a compact connected orientable surface S there are two fundamental objects attached: a group and a space. The group is the mapping class group of S, denoted by Mod(S). This group is defined by
Profinite Teichmüller theory
For 2g – 2 + n > 0, let Γg, n be the Teichmuller group of a compact Riemann surface of genus g with n points removed Sg, n , i.e., the group of homotopy classes of diffeomorphisms of Sg, n which
Fundamental groups of moduli stacks of stable curves of compact type
Mg;n , for 2g 2Cn> 0, be the moduli stack of n‐pointed, genus g , stable complex curves of compact type. Various characterizations and properties are obtained of both the topological and algebraic
For 2g − 2 + n > 0, the Teichmüller modular group Γg,n of a compact Riemann surface of genus g with n points removed, Sg,n is the group of homotopy classes of diffeomorphisms of Sg,n which preserve
Galois Covers of Moduli of Curves
Moduli spaces of pointed curves with some level structure are studied. We prove that for so-called geometric level structures, the levels encountered in the boundary are smooth if the ambient variety
The faithfulness of the monodromy representations associated with certain families of algebraic curves
Abstract We consider the faithfulness of the monodromy representation associated with the universal family of n -pointed algebraic curves of genus g (2−2 g − n ρ g , n of the representation to the