Injections of mapping class groups

Aramayona, Javier¹ ; Leininger, Christopher J² ; Souto, Juan³

¹ School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
² Department of Mathematics, University of Illinois, Urbana–Champaign, IL 61801, USA
³ Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA

Geometry & topology, Tome 13 (2009) no. 5, pp. 2523-2541.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.2523

Keywords: mapping class group, homomorphism, surface, monomorphism

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