Automorphisms of the mapping class group of a nonorientable surface

Abstract

Let $S$ be a nonorientable surface of genus $g\ge 5$ with $n\ge 0$ punctures, and $\Mcg(S)$ its mapping class group. We define the complexity of $S$ to be the maximum rank of a free abelian subgroup of $\Mcg(S)$. Suppose that $S_1$ and $S_2$ are two such surfaces of the same complexity. We prove that every isomorphism $\Mcg(S_1)\to\Mcg(S_2)$ is induced by a diffeomorphism $S_1\to S_2$. This is an analogue of Ivanov's theorem on automorphisms of the mapping class groups of an orientable surface, and also an extension and improvement of the first author's previous result.

21 pages, 10 figures, revision and corrections, to appear in Geometriae Dedicata

References in corpus (1)

• Presentations for the punctured mapping class groups in terms of Artin groups

Cited by in corpus (1)

• An algebraic characterization of a Dehn twist for nonorientable surfaces