Math 257 - Kleinian groups

Instructor: Ian Agol
Lectures: MWF 11-12, 7 Evans
Course Control Number:
Office: 921 Evans
Office Hours: M 2-3, W 3-4

Textbook:
Outer Circles, Albert Marden

Homework:
Pick a few exercises from Chapter 1 by Friday 9/2.
On Friday, we'll assign each of you an exercise.
Work it out, and give a presentation on it on it Friday 9/9.

Chapter 2 Exercise presentations on Monday, October 3.

Appolonian gasket

Tessellations

Dimensions film

Recommended:

Thurston, The Geometry and Topology of 3-manifolds

Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry

Mumford, Series, Wright, Indra's Pearls

Kapovich, Hyperbolic manifolds and discrete groups

Ratcliffe, Foundations of hyperbolic manifolds

Maskit, Kleinian groups

Fundamentals of hyperbolic manifolds

A crash course in Kleinian groups, Bers-Kra Eds.

Survey articles:

Bonahon, The geometry of Teichmüller space via geodesic currents

Canary, Marden's tameness conjecture, history and applications

Pushing the boundary

Covering theorems for hyperbolic 3-manifolds

Geometrically tame hyperbolic 3-manifolds

Minsky, End invariants and the classification of hyperbolic 3-manifolds

Bowditch's preprints:
Coarse hyperbolic models for 3-manifolds
Surface group actions and length bounds
End invariants of hyperbolic 3-manifolds
Geometric models for hyperbolic 3-manifolds
Notes on tameness
Tight geodesics in the curve complex
Length bounds on curves arising from tight geodesics

Juan Souto: SHORT GEODESICS IN HYPERBOLIC COMPRESSION
BODIES ARE NOT KNOTTED

Related Reading:

MacLachlan and Reid, Arithmetic of hyperbolic 3-manifolds

Syllabus:
The topic this semester will be Kleinian groups, discrete finitely generated subgroups of PSL_2(C).
Recently, the classification of these groups has been accomplished in terms of topological and conformal data.
Topics will include 3-manifold theory, the measurable Riemann mapping theorem,
currents and laminations on surfaces, pleated surfaces in hyperbolic 3-manifolds,
geometric tameness, the covering theorem, and the Ahlfors measure conjecture.
If there's time, we'll survey the curve complex and the ending lamination theorem,
and the orbifold and geometrization theorems.