Math 8803 Low-dimensional Topology and Hyperbolic Geometry Fall 2014 -	------------------------------Theodor Geisel
News: Welcome to Math 8803!

Geometry of the Complex of Curves
Week	Dates	Topics	Reading	Lectures	Notes
10	Oct 21	Overview / Hyperbolicity	Sisto	Week 10
11	Oct 28	Axes / Free groups	MMI	Week 11
12	Nov 4	BGI	Webb	Week 12
13	Nov 11	pA Recipe	Mangahas Guirardel	Week 13
14	Nov 18	Tight geodesics	Masur-Minsky II	Week 14
15	Nov 25	Acylindricity	Webb	Week 15	Thanksgiving
16	Dec 2	RAAGs	CLM	Week 16
				Weeks 10-16

References

---Combinatorial cubings, cusps, and the dodecahedral knots, I.R. Aitchison and J.H. Rubinstein

---Geometric group theory and 3-manifolds hand in hand: the fulfillment of Thurston's vision, Mladen Bestvina

---Geometric structures on 3-manifolds, Francis Bonahon

---Seifert fibered spaces, Matthew Brin

---Notes on 3-manifolds, Danny Calegari

---Hyperbolic geometry, James W. Cannon, William J. Floyd, Richard Kenyon, and Walter R. Parry

---The CompuTop.org Software Archive

---An introduction to 3-manifolds, Stefan Friedl

---Hyperbolic Geometry and 3-Manifold Topology, David Gabai

---Hyperbolic 3-manifolds in the 2000's, David Gabai

---Hyperbolic manifolds according to Thurston and Jorgensen, Mikhail Gromov

---Introduction to hyperbolic geometry, Subhojoy Gupta

---Notes on Basic 3-manifolds, Allen Hatcher

---The classification of 3-manifolds - a brief overview, Allen Hatcher

---The classification of 3-manifolds, Allen Hatcher

---The homeomorphism problem: classification of 3-manifolds, William Jaco

---Hyperbolic manifolds and discrete groups: Lectures on Thurston's geometrization, Misha Kapovich

---Knots and Manifolds, Louis Kauffman

---Three-dimensional manifolds, Marc Lackenby

---Hyperbolic Manifolds, Marc Lackenby

---From metrics to moduli space, Chris Leininger

---Outer circles: an introduction to hyperbolic 3-manifolds, Albert Marden

---Towards the Poincare conjecture and the classification of 3-manifolds, John Milnor

---Around the Borromean link, Jose Maria Montesinos-Amilibia

---Notes on Geometry and 3-manifolds, Walter Neumann

---Lectures on Seifert manifolds, Walter Neumann

---Hyperbolic knot theory, Jessica Purcell

---Foundations of hyperbolic manifolds, John Ratcliffe

---Three manifolds, Saul Schleimer

---The geometries of 3-manifolds, Peter Scott

---Hyperbolic geometry, Caroline Series

---The Geometry and Topology of 3-manifolds, William Thurston

---The mystery of 3-manifolds, William Thurston

---Three dimensional manifolds, Kleinian groups and hyperbolic geometry, William Thurston

---Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle, William Thurston

---How to see 3-manifolds, William Thurston

---Complex of curves

---Uniform hyperbolicity of the graphs of curves, Tarik Aougab

---Quasi-homomorphisms on mapping class groups, Mladen Bestvina and Koji Fujiwara

---Intersection numbers and the hyperbolicity of the curve complex , Brian Bowditch

---Tight geodesics in the curve complex, Brian Bowditch

---Length bounds on curves arising from tight geodesics, Brian Bowditch

---Uniform hyperbolicity of the curve graphs, Brian Bowditch

---The classification of Kleinian surface groups II: the ending lamination conjecture, Jeff Brock, Dick Canary, and Yair Minsky

---The geometry of right angled Artin subgroups of mapping class groups, Matt Clay, Chris Leininger, and Johanna Mangahas

---Uniform hyperbolicity of the curve graph via surgery sequences, Matt Clay, Kasra Rafi, and Saul Schleimer

---Rotating families, Dehn fillings and small cancellation, Vincent Guirardel ---Boundary structure of the modular group, William J. Harvey

---Mapping class groups, Nikolai Ivanov

---Automorphisms of Complexes of Curves and of Teichmüller Spaces, Nikolai Ivanov

---A finite set of generators for the homeotopy group of a 2-manifold, W.B.R. Lickorish

---A recipe for short-word pseudo-Anosovs, Johanna Mangahas

---Geometry of the complex of curves I: hyperbolicity, Howard Masur and Yair Minsky

---Geometry of the complex of curves II: hierarchical structure, Howard Masur and Yair Minsky

---Curve complexes, surfaces and 3-manifolds, Yair Minsky

---The classification of Kleinian surface groups, I: models and bounds, Yair Minsky

---Notes on the complex of curves, Saul Schleimer

---Combinatorial rigidity in curve complexes and mapping class groups, Ken Shackleton

---Lecture Notes on Braids and Dynamics, Jean-Luc Thiffeault

---1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs, Richard Webb, Sebastian Hensel, and Piotr Przytycki

---Uniform bounds for bounded geodesic image theorems, Richard Webb

---Combinatorics of tight geodesics and stable lengths, Richard Webb

Topics for Student Seminars

---The uniformization theorem

---The loop theorem

---The sphere theorem

---Classification of Seifert manifolds

---JSJ decompositions of groups

---Automorphisms of the complex of curves

---Cartan--Hadamard theorem

---Fenchel--Nielsen coordinates

---SnapPy

---Nielsen-Thurston classification theorem

---Dehn-Nielsen-Baer theorem

---Quasi-morphisms on mapping class groups

---Asymptotic dimension of the mapping class group

---Bestvina-Handel algorithm

---Boundary of the complex of curves

---Ending lamination theorem

Resources

---Georgia Tech Honor Code