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Shrinkwrapping and the taming of hyperbolic 3-manifolds : preprint
We introduce a new technique for finding CAT(-1) surfaces in hyperbolic 3-manifolds. We use this to show that a complete hyperbolic 3-manifold with finitely generated fundamental group is
Thermodynamic Formalism
These are introductory notes on the thermodynamical formalism, with application to topics in dynamics and geometric group theory. These notes are based on a graduate course co-taught with Amie
Laminations and groups of homeomorphisms of the circle
Abstract.If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that π1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions
Stable commutator length is rational in free groups
For any group, there is a natural (pseudo-)norm on the vector space B^H_1 of real homogenized (group) 1 -boundaries, called the stable commutator length norm. This norm is closely related to, and can
Foliations and the Geometry of 3-Manifolds
Preface 1. Surface bundles 2. The topology of S1 3. Minimal surfaces 4. Taut foliations 5. Finite depth foliations 6. Essential laminations 7. Universal circles 8. Constructing transverse laminations
Stable commutator length in word-hyperbolic groups
In this paper we obtain uniform positive lower bounds on the stable commutator length of elements in word-hyperbolic groups and certain groups acting on hyperbolic spaces (namely the mapping class
Distortion in transformation groups
We exhibit rigid rotations of spheres as distortion elements in groups of diffeomorphisms, thereby answering a question of J Franks and M Handel. We also show that every homeomorphism of a sphere is,
Faces of the scl norm ball
Let F be the fundamental group of S, where S is a compact, connected, oriented surface with negative Euler characteristic and nonempty boundary. (1) The projective class of the chain \partial S in
This book is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric
Statistics and compression of scl
Abstract We obtain sharp estimates on the growth rate of stable commutator length on random (geodesic) words, and on random walks, in hyperbolic groups and groups acting non-degenerately on