Journal of the Mathematical Society of Japan

Automorphisms of the Torelli complex and the complex of separating curves

Yoshikata KIDA

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Abstract

We compute the automorphism groups of the Torelli complex and the complex of separating curves for all but finitely many compact orientable surfaces. As an application, we show that the abstract commensurators of the Torelli group and the Johnson kernel for such surfaces are naturally isomorphic to the extended mapping class group.

Article information

Source
J. Math. Soc. Japan, Volume 63, Number 2 (2011), 363-417.

Dates
First available in Project Euclid: 25 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1303737792

Digital Object Identifier
doi:10.2969/jmsj/06320363

Mathematical Reviews number (MathSciNet)
MR2793105

Zentralblatt MATH identifier
1378.57027

Subjects
Primary: 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]
Secondary: 20F38: Other groups related to topology or analysis

Keywords
the Torelli complex the complex of separating curves the Torelli group the Johnson kernel

Citation

KIDA, Yoshikata. Automorphisms of the Torelli complex and the complex of separating curves. J. Math. Soc. Japan 63 (2011), no. 2, 363--417. doi:10.2969/jmsj/06320363. https://projecteuclid.org/euclid.jmsj/1303737792


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