Congruence topologies on the mapping class group
نویسندگان
چکیده
منابع مشابه
The Torelli group and congruence subgroups of the mapping class group
Let Σg,n be a compact oriented genus g surface with n boundary components. The mapping class group of Σg,n, denoted Modg,n, is the group of orientation-preserving diffeomorphisms of Σg,n that restrict to the identity on ∂Σg,n, modulo isotopies that fix ∂Σg,n. The group Modg,n plays a fundamental role in many areas of mathematics, ranging from low-dimensional topology to algebraic geometry. At l...
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Deformation spaces Hom(π,G)/G of representations of the fundamental group π of a surface Σ in a Lie group G admit natural actions of the mapping class group ModΣ, preserving a Poisson structure. When G is compact, the actions are ergodic. In contrast if G is noncompact semisimple, the associated deformation space contains open subsets containing the Fricke-Teichmüller space upon which ModΣ acts...
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These notes are based on lectures given at Zhejiang University, July 14–20, 2008. My goal was to present some analytic techniques that can be used to study the action of the mapping class group on the representations varieties of surface groups. The subject has been quite active of late. For more information – and more complete coverage of recent work – I refer the interested reader to the intr...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.11.004