The hyperelliptic mapping class group of a nonorientable surface of genus $g\geq 4$ has a faithful representation into $GL(g^2-1,\mathbb{R})$

TL;DR

This paper demonstrates that the hyperelliptic mapping class group of a nonorientable surface with genus at least 4 can be faithfully represented as a linear group of dimension g^2-1 over the real numbers.

Contribution

It establishes the existence of a faithful linear representation for the hyperelliptic mapping class group of nonorientable surfaces of genus g ≥ 4.

Findings

Faithful representation exists for genus g ≥ 4

Dimension of representation is g^2 - 1

Representation over the real numbers

Abstract

We prove that the hyperelliptic mapping class group of a nonorientable surface of genus $g\geq 4$ has a faithful linear representation of dimension $g^2-1$ over $\mathbb{R}$.