English

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 ϕ\phi 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 ϕ\phi.

Keywords

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

R2 v1 2026-07-01T06:38:50.343Z