Automorphisms of the loop and arc graph of an infinite-type surface
Geometric Topology
2019-12-17 v1 Group Theory
Abstract
We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a finite set of punctures is isomorphic to the arc graph relative to that finite set of punctures. This extends a known result for sufficiently complex finite-type surfaces, and provides a new angle from which to study the mapping class groups of infinite-type surfaces.
Cite
@article{arxiv.1912.06774,
title = {Automorphisms of the loop and arc graph of an infinite-type surface},
author = {Anschel Schaffer-Cohen},
journal= {arXiv preprint arXiv:1912.06774},
year = {2019}
}