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Injections of mapping
class groups
Javier Aramayona, Christopher J Leininger and Juan Souto |
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Geometry & Topology 13 (2009) 2523–2541
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Abstract |
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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. |
Keywords
mapping class group, homomorphism, surface, monomorphism
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Mathematical Subject Classification 2000
Primary: 57M07, 20F34
Secondary: 57M60, 30F60, 32G15, 57R50
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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
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Authors |
| Javier Aramayona | |
| School of Mathematics, Statistics
and Applied Mathematics National University of Ireland Galway Ireland |
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| Christopher J Leininger | |
| Department of Mathematics University of Illinois Urbana–Champaign, IL 61801 USA |
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| Juan Souto | |
| Department of Mathematics University of Michigan Ann Arbor, MI 48109 USA |
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