The mapping class group action on -character varieties
نویسندگان
چکیده
منابع مشابه
The Action of the Mapping Class Group on Representation Varieties
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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We extend the definition of algebraic entropy to endomorphisms of affine varieties. We calculate algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we call the spectral radius, a generalization of the dilatation of a Pseudo-Anosov mapping class. Our calculations are compatible with all known calculations of...
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When G is a connected compact Lie group, and π is a closed surface group, then Hom(π,G)/G contains an open dense Out(π)-invariant subset which is a smooth symplectic manifold. This symplectic structure is Out(π)-invariant and therefore defines an invariant measure μ, which has finite volume. The corresponding unitary representation of Out(π) on L(Hom(π,G)/G, μ) contains no finite-dimensional su...
متن کاملErgodicity of Mapping Class Group Actions on Su(2)-character Varieties
Let be a compact orientable surface with genus g and n boundary components ∂1, . . . , ∂n. Let b = (b1, . . . , bn) ∈ [−2, 2]n. Then the mapping class group Mod( ) acts on the relative SU(2)-character varietyXb := Homb(π , SU(2))/SU, comprising conjugacy classes of representations ρ with tr(ρ(∂i)) = bi. This action preserves a symplectic structure on the open dense smooth submanifold of Homb(π ...
متن کاملErgodicity of Mapping Class Group Actions on Su(2)-character Varieties
Let Σ be a compact orientable surface with genus g and n boundary components ∂1, . . . , ∂n. Let b = (b1, . . . , bn) ∈ [−2, 2]. Then the mapping class groupMod(Σ) acts on the relative SU(2)-character variety Xb := Homb(π, SU(2))/SU(2), comprising conjugacy classes of representations ρ with tr(ρ(∂i)) = bi. This action preserves a symplectic structure on the open dense smooth submanifold of Homb...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2020
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2020.50