Geometry & Topology

Injections of mapping class groups

Javier Aramayona, Christopher J Leininger, and Juan Souto

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We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on mapping class groups of once-punctured surfaces and have quite curious behaviour. For instance, some pseudo-Anosov elements are mapped to multitwists. Neither of these two types of phenomena were previously known to be possible although the constructions are elementary.

Article information

Geom. Topol., Volume 13, Number 5 (2009), 2523-2541.

Received: 24 November 2008
Revised: 15 June 2009
Accepted: 28 May 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M07: Topological methods in group theory 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
Secondary: 57M60: Group actions in low dimensions 30F60: Teichmüller theory [See also 32G15] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 57R50: Diffeomorphisms

mapping class group homomorphism surface monomorphism


Aramayona, Javier; Leininger, Christopher J; Souto, Juan. Injections of mapping class groups. Geom. Topol. 13 (2009), no. 5, 2523--2541. doi:10.2140/gt.2009.13.2523.

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