Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

P-2021-05

Gaëtan Borot, Séverin Charbonnier, Vincent Delecroix, Alessandro Giacchetto, Campbell Wheeler

 

AROUND THE COMBINATORIAL UNIT BALL OF MEASURED FOLIATIONS ON BORDERED SURFACES

 

Abstract: The volume Bcomb(G) of the unit ball — with respect to the combinatorial length function lG — Σ 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

(Bcomb)s, as a function over the combinatorial moduli spaces, is integrable with respect to the Σ

Kontsevich measure. The results depends on the topology of Σ, in contrast with the situation for hyperbolic surfaces where [6] recently proved an optimal square-integrability.

 

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2021-05

 

35 pp.