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On a function on the mapping class group of a surface of genus 2

✍ Scribed by Ryoji Kasagawa

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 184 KB
Volume: 102
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00157-6

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✦ Synopsis

We study representations of subgroups of the mapping class group M g of a surface of genus g 2 arising from the actions of them on the first cohomology groups of the surface with local coefficient systems which are defined by nontrivial homomorphisms π 1 (Σ g , * ) → Z 2 = Aut(Z). As an application, in the case of g = 2, we construct a function on M 2 which agrees with the Meyer function φ : M 2 → Q on the Torelli group J 2 .

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Partially supported by the research funds of Ministero dell'Uni¨ersita e della Ricerca Scientifica e Tecnologica and by Grant 9300856.CT01 of Consiglio Nazionale delle Ricerche.