Kasra Rafi

A characterization of short curves of a Teichmuller geodesic

We provide a combinatorial condition characterizing curves that are short along a Teichmuller geodesic. This condition is closely related to the condition pro- vided by Minsky for curves in a hyperbolic 3-manifold to be short. We show that short curves in a hyperbolic manifold homeomorphic to S×R are also short in the corresponding Teichmuller geodesic, and we provide examples demon- strating that the converse is not true.

On hyperbolicity of free splitting and free factor complexes

We show how to derive hyperbolicity of the free factor complex of

Uniform hyperbolicity of the curve graph via surgery sequences

F_N

Hyperbolicity in Teichmüller space

from the Handel-Mosher proof of hyperbolicity of the free splitting complex of

COVERS AND THE CURVE COMPLEX

F_N

Length spectra and degeneration of flat metrics

, thus obtaining an alternative proof of a theorem of Bestvina-Feighn. We also show that under the natural map

CURVE COMPLEXES ARE RIGID

\tau

Large-scale rank of Teichmüller space

from the free splitting complex to free factor complex, a geodesic

LIMIT SETS OF TEICHM ULLER GEODESICS WITH MINIMAL NONUNIQUELY ERGODIC VERTICAL FOLIATION, II

[x,y]

Algebraic ending laminations and quasiconvexity

maps to a path that is uniformly Hausdorff-close to a geodesic