Counting mapping class group orbits under shearing coordinates
نویسندگان
چکیده
Let \(S_{g,n}\) be an oriented surface of genus g with n punctures, where \(2g-2+n>0\) and \(n>0\). Any ideal triangulation induces a global parametrization the Teichmüller space \(\mathcal {T}_{g,n}\) called shearing coordinates. We study asymptotics number mapping class group orbits respect to standard Euclidean norm The result is based on works Mirzakhani.
منابع مشابه
Counting Orbits Under Kreweras Complementation
The Kreweras complementation map is an anti-isomorphism on the lattice of noncrossing partitions. We consider an analogous operation for plane trees motivated by the molecular biology problem of RNA folding. In this context, we explicitly count the orbits of Kreweras’ map according to their length as the number of appropriate symmetry classes of trees in the plane. These new enumeration results...
متن کاملExceptional Discrete Mapping Class Group Orbits in Moduli Spaces
Let M be a four-holed sphere and Γ the mapping class group of M fixing ∂M . The group Γ acts on the space MB(SU(2)) of SU(2)-gauge equivalence classes of flat SU(2)-connections on M with fixed holonomy on ∂M . We give examples of flat SU(2)connections whose holonomy groups are dense in SU(2), but whose Γ-orbits are discrete in MB(SU(2)). This phenomenon does not occur for surfaces with genus gr...
متن کاملCounting the Orbits on Finite Simple Groups under the Action of the Automorphism Group - Suzuki Groups vs. Linear Groups
We determine the number ω(G) of orbits on the (finite) group G under the action of Aut(G) for G ∈ {PSL(2, q),SL(2, q),PSL(3, 3),Sz(2)}, covering all of the minimal simple groups as well as all of the simple Zassenhaus groups. This leads to recursive formulae on the one hand, and to the equation ω(Sz(q)) = ω(PSL(2, q)) + 2 on the other. MSC 20E32, 20F28, 20G40, 20-04
متن کاملEstimation under group actions: recovering orbits from invariants
Motivated by geometric problems in signal processing, computer vision, and structural biology, we study a class of orbit recovery problems where we observe noisy copies of an unknown signal, each acted upon by a random element of some group (such as Z/p or SO(3)). The goal is to recover the orbit of the signal under the group action. This generalizes problems of interest such as multi-reference...
متن کاملDeterminants of Sum of Orbits under Compact Lie Group
We study the determinants on the sum of orbits of two elements in the Lie algebra of a compact connected subgroup in the unitary group. As an application, the extremal determinant expressions are obtained for the symplectic group.
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: Geometriae Dedicata
سال: 2022
ISSN: ['0046-5755', '1572-9168']
DOI: https://doi.org/10.1007/s10711-022-00674-x