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Injective homomorphisms of mapping class groups of non-orientable surfaces
- Publication Year :
- 2017
-
Abstract
- Let $N$ be a compact, connected, non-orientable surface of genus $\rho$ with $n$ boundary components, with $\rho \ge 5$ and $n \ge 0$, and let $\mathcal{M} (N)$ be the mapping class group of $N$. We show that, if $\mathcal{G}$ is a finite index subgroup of $\mathcal{M} (N)$ and $\varphi: \mathcal{G} \to \mathcal{M} (N)$ is an injective homomorphism, then there exists $f_0 \in \mathcal{M} (N)$ such that $\varphi (g) = f_0 g f_0^{-1}$ for all $g \in \mathcal{G}$. We deduce that the abstract commensurator of $\mathcal{M} (N)$ coincides with $\mathcal{M} (N)$.
- Subjects :
- Mathematics - Geometric Topology
Mathematics - Group Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1708.00218
- Document Type :
- Working Paper