Volume 13, issue 5 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Injections of mapping class groups

Javier Aramayona, Christopher J Leininger and Juan Souto

Geometry & Topology 13 (2009) 2523–2541
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.

Keywords
mapping class group, homomorphism, surface, monomorphism
Mathematical Subject Classification 2000
Primary: 57M07, 20F34
Secondary: 57M60, 30F60, 32G15, 57R50
References
Publication
Received: 24 November 2008
Revised: 15 June 2009
Accepted: 28 May 2009
Published: 2 July 2009
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Shigeyuki Morita
Authors
Javier Aramayona
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
Galway
Ireland
Christopher J Leininger
Department of Mathematics
University of Illinois
Urbana–Champaign, IL 61801
USA
Juan Souto
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109
USA