Let Image be a fibered face of the Thurston norm ball for a hyperbolic 3-manifold M. Any Image determines a measured foliation Image of M. Generalizing the case of Teichmüller geodesics and fibrations, we show Image ...

Let {Delta} sub C denote the unit disk, viewed as a model for the hyperbolic plane. Under rescaling, {Delta} takes on the appearance of a tree, with an additional ribbon structure coming from the cyclic ordering of its ...

In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of \(n\) mod 360, and come exclusively from spherical subdiagrams.

This paper classifies orbit closures and invariant measures for the natural action of SL2(ℝ) on Ωℳ2, the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two.

The Hilbert modular surface \(X_D\) is the moduli space of Abelian varieties A with real multiplication by a quadratic order of discriminant \(D > 1\). The locus where A is a product of elliptic curves determines a finite ...

Let A ⊂ SLn(R) be the diagonal subgroup, and identify SLn(R)/SLn(Z)with the space of unimodular lattices in Rn. In this paper we show that the closure of any bounded orbit A • L ⊂ SLn(R)/SLn(Z)meets the set of well-rounded ...