Irreducible Sp-representations and subgroup distortion in the mapping class group
نویسندگان
چکیده
We prove that various subgroups of the mapping class group Mod(Σ) of a surface Σ are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenstädt), the “point-pushing” and surface braid subgroups, and the Lagrangian subgroup. Our techniques include a method to compute lower bounds on distortion via representation theory and an extension of Johnson theory to arbitrary subgroups of H1(Σ;Z).
منابع مشابه
Monomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
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...
متن کاملDistinguished positive regular representations
Let $G$ be a tamely ramified reductive $p$-adic group. We study distinction of a class of irreducible admissible representations of $G$ by the group of fixed points $H$ of an involution of $G$. The representations correspond to $G$-conjugacy classes of pairs $(T,phi)$, where $T$ is a tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter of $T$ whose restriction t...
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007