• Corpus ID: 239769021

Around the combinatorial unit ball of measured foliations on bordered surfaces

@inproceedings{Borot2021AroundTC,
  title={Around the combinatorial unit ball of measured foliations on bordered surfaces},
  author={Gaetan Borot and S'everin Charbonnier and Vincent Delecroix and Alessandro Giacchetto and Campbell Wheeler},
  year={2021}
}
The volume B Σ (G) of the unit ball — with respect to the combinatorial length function lG — of the space of measured foliations on a stable bordered surface Σ appears as the prefactor of the polynomial growth of the number of multicurves on Σ. We find the range of s ∈ R for which (B Σ ) , as a function over the combinatorial moduli spaces, is integrable with respect to the Kontsevich measure. The results depends on the topology of Σ, in contrast with the situation for hyperbolic surfaces where… 

Figures from this paper

References

SHOWING 1-10 OF 30 REFERENCES
Tiling the projective foliation space of a punctured surface
There is a natural way to associate7 to each ideal triangulation of a punctured surface a cell decomposition of the projective foliation space of the punctured surface. A recent theme in the topology
Thurston's Work on Surfaces
This book is an exposition of Thurston’s theory of surfaces: measured foliations, the compactification of Teichmuller space and the classification of diffeomorphisms. The mathematical content is
Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of
Topological recursion for Masur-Veech volumes.
We study the Masur--Veech volumes $MV_{g,n}$ of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures. We show that the volumes
The decorated Teichmüller space of punctured surfaces
A principal ℝ+5-bundle over the usual Teichmüller space of ans times punctured surface is introduced. The bundle is mapping class group equivariant and admits an invariant foliation. Several
On the Kontsevich geometry of the combinatorial Teichmüller space
We study the combinatorial Teichm\"uller space and construct on it global coordinates, analogous to the Fenchel-Nielsen coordinates on the ordinary Teichm\"uller space. We prove that these
Triangulated Riemann surfaces with boundary and the Weil-Petersson Poisson structure
Given a hyperbolic surface with geodesic boundary S, the lengths of a maximal system of disjoint simple geodesic arcs on S that start and end at ∂S perpendicularly are coordinates on the Teichmuller
Hurwitz theory of elliptic orbifolds, I
An elliptic orbifold is the quotient of an elliptic curve by a finite group. In 2001, Eskin and Okounkov proved that generating functions for the number of branched covers of an elliptic curve with
On Teichmüller spaces of surfaces with boundary
We characterize hyperbolic metrics on compact triangulated surfaces with boundary using a variational principle. As a consequence, a new parameterization of the Teichmüller space of a compact surface
Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials
In this paper we analyze the large genus asymptotics for intersection numbers between $\psi$-classes, also called correlators, on the moduli space of stable curves. Our proofs proceed through a
...
1
2
3
...