Geometry & Topology
- Geom. Topol.
- Volume 13, Number 5 (2009), 2523-2541.
Injections of mapping class groups
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.
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
Permanent link to this document
Digital Object Identifier
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
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