SIMPLE CURRENT EXTENSIONS AND MAPPING CLASS GROUP REPRESENTATIONS
نویسندگان
چکیده
منابع مشابه
Groupoid Extensions of Mapping Class Representations for Bordered Surfaces
The mapping class group of a surface with one boundary component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class group can be identified with the fundamental group of Riemann’s moduli space, it is furthermore identified with a subgroup of the fundamental path groupoid upo...
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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...
متن کاملActions and irreducible representations of the mapping class group
Let G be a countable discrete group. Call two subgroups H1 and H2 of G commensurable if H1 ∩H2 has finite index in both H1 and H2. We say that an action of G on a discrete set X has noncommensurable stabilizers if the stabilizers of any two distinct points of X are not commensurable. We prove in this paper that the action of the mapping class group on the complex of curves has noncommensurable ...
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Let Γg be the fundamental group of a closed oriented Riemann surface Σg, g ≥ 2, and let G be a simple Lie group of Hermitian type. The Toledo invariant defines the subset of maximal representations Repmax(Γg , G) in the representation variety Rep(Γg , G). Repmax(Γg, G) is a union of connected components with similar properties as Teichmüller space T (Σg) = Repmax(Γg , PSL(2, R)). We prove that ...
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A well-known conjecture asserts that the mapping class group of a surface (possibly with punctures/boundary) does not virtually surject onto Z if the genus of the surface is large. We prove that if this conjecture holds for some genus, then it also holds for all larger genera. We also prove that if there is a counterexample to this conjecture, then there must be a counterexample of a particular...
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ژورنال
عنوان ژورنال: International Journal of Modern Physics A
سال: 1998
ISSN: 0217-751X,1793-656X
DOI: 10.1142/s0217751x9800007x