Mapping class group dynamics on \mathrm{Aff}(\mathbb{C})-characters.
نویسندگان
چکیده
منابع مشابه
Dynamics of the Mapping Class Group Action on the Variety of Psl2 C Characters
We study the action of the mapping class groupMod(S) on the boundary ∂Q of quasifuchsian space Q. Among other results, Mod(S) is shown to be topologically transitive on the subset C ⊂ ∂Q of manifolds without a conformally compact end. We also prove that any open subset of the character varietyX (π1(S),PSL2 C) intersecting ∂Q does not admit a nonconstant Mod(S)-invariant meromorphic function. Th...
متن کاملMapping Class Group Dynamics on Surface Group Representations
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 کاملMapping Class Group Actions on Quantum Doubles
We study representations of the mapping class group of the punctured torus on the double of a finite dimensional possibly non-semisimple Hopf algebra that arise in the construction of universal, extended topological field theories. We discuss how for doubles the degeneracy problem of TQFT’s is circumvented. We find compact formulae for the S±1-matrices using the canonical, non degenerate forms ...
متن کاملRandom walks on the mapping class group
We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli group.
متن کاملDynamics of the Mapping Class Group on the Moduli of a Punctured Sphere with Rational Holonomy
Let M be a four-holed sphere and Γ the mapping class group of M fixing the boundary ∂M . The group Γ acts on MB(SL(2,C)) = Hom+B (π1(M), SL(2,C))/ SL(2,C) which is the space of completely reducible SL(2,C)-gauge equivalence classes of flat SL(2,C)-connections on M with fixed holonomy B on ∂M . Let B ∈ (−2, 2) and MB be the compact component of the real points of MB(SL(2,C)). These points corres...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2016
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.3024