## Geometry & Topology

### Injections of mapping class groups

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800318

Digital Object Identifier
doi:10.2140/gt.2009.13.2523

Mathematical Reviews number (MathSciNet)
MR2529941

Zentralblatt MATH identifier
1225.57001

#### Citation

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. https://projecteuclid.org/euclid.gt/1513800318

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