IDEAL CELL-DECOMPOSITIONS FOR A HYPERBOLIC SURFACE AND EULER CHARACTERISTIC

Exponentiation and Euler Characteristic

A Formula for the Euler Characteristic Of

In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves. The proof relies on quite elementary methods , such as the enumeration of the graphs involved in a suitable stratification of M 2,n .

Dimension and Ergodic Decompositions for Hyperbolic Flows

For conformal hyperbolic flows, we establish explicit formulas for the Hausdorff dimension and for the pointwise dimension of an arbitrary invariant measure. We emphasize that these measures are not necessarily ergodic. The formula for the pointwise dimension is expressed in terms of the local entropy and of the Lyapunov exponents. We note that this formula was obtained before only in the speci...

Large deviations and moments for the Euler characteristic of a random surface

We study random surfaces constructed by glueing together N/k filled k-gons along their edges, with all (N − 1)!! = (N − 1)(N − 3) · · · 3 · 1 pairings of the edges being equally likely. (We assume that lcm{2, k} divides N .) The Euler characteristic of the resulting surface is related to the number of cycles in a certain random permutation of {1,. .. , N }. Gamburd has shown that when 2 lcm{2, ...

Ideal Bicombings for Hyperbolic Groups and Applications

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [MSb] hold for all non-elementary hyperbolic groups and thei...