Representation varieties and genus-three Torelli maps
Geometric Topology
2025-10-16 v1
Abstract
We consider the family of Torelli homeomorphisms on a genus-three surface given by powers of a fixed bounding pair map. For each such homeomorphism we determine the number of connected components of the fixed point set of the induced map on the representation variety of the surface, as well as the number of connected components of the representation variety of the mapping torus of .
Cite
@article{arxiv.2510.13491,
title = {Representation varieties and genus-three Torelli maps},
author = {Allen Bao and Anunoy Chakraborty and David L. Duncan and Jordan Larson and Kelson McBride},
journal= {arXiv preprint arXiv:2510.13491},
year = {2025}
}
Comments
14 pages, 2 figures. Comments welcome