Automorphisms of the mapping class group of a nonorientable surface

2014/03/11 by Ferihe Atalan, Błażej Szepietowski, Atalan, Ferihe +1
Computer Science · Mathematics · #20F38 #57N05 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1403.2774

openalex publication_date 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a nonorientable surface of genus g≥ 5 with n≥ 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 S₁ and S₂ are two such surfaces of the same complexity. We prove that every isomorphism \Mcg(S₁)→\Mcg(S₂) is induced by a diffeomorphism S₁→ S₂. 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.

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