Journal of the Mathematical Society of Japan

Commensurators of surface braid groups

Yoshikata KIDA and Saeko YAMAGATA

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We prove that if g and n are integers at least two, then the abstract commensurator of the braid group with n strands on a closed orientable surface of genus g is naturally isomorphic to the extended mapping class group of a compact orientable surface of genus g with n boundary components.

Article information

J. Math. Soc. Japan, Volume 63, Number 4 (2011), 1391-1435.

First available in Project Euclid: 27 October 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
Secondary: 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45] 20F36: Braid groups; Artin groups

surface braid groups mapping class groups


KIDA, Yoshikata; YAMAGATA, Saeko. Commensurators of surface braid groups. J. Math. Soc. Japan 63 (2011), no. 4, 1391--1435. doi:10.2969/jmsj/06341391.

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