9 papers
Totally symmetric sets in the general linear group
Noah Caplinger, Nick Salter
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homom…
Simple closed curves in stable covers of surfaces
Nick Salter
Let be a regular covering of a surface of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group . We give necessary and suf…
Global fixed points of mapping class group actions and a theorem of Markovic
Lei Chen, Nick Salter
We give a short and elementary proof of the non-realizability of the mapping class group via homeomorphisms. This was originally established by Markovic, resolving a conjecture of…
Framed mapping class groups and the monodromy of strata of Abelian differentials
Aaron Calderon, Nick Salter
This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Bui…
Relative homological representations of framed mapping class groups
Aaron Calderon, Nick Salter
Let be a surface with either boundary or marked points, equipped with an arbitrary framing. In this note we determine the action of the associated "framed mapping class group"…
Linear-central filtrations and the image of the Burau representation
Nick Salter
The Burau representation is a fundamental bridge between the braid group and diverse other topics in mathematics. A 1974 question of Birman asks for a description of the image; in…