## Course Information for Math 595 GTG, Geometric Topology
Spring 2016

**Instructor information:**
**Instructor:** Chris Leininger.
**Email:** clein [AT] math.uiuc.edu,
**Phone:** 265-6763.

**Office:** 366 Altgeld Hall.
**Office hours:** By appointment

**Textbook: ** None required, but the following references will be
useful (I will add more later).
- Thurston, William P.,
*The Geometry and Topology of
Three-Manifolds*, aka *Thurston's notes*. Here are Chapters
1,
2,
3,
4,
5,
6,
7,
8,
9,
11,
13.
- Thurston, William P.,
*Three-Dimensional Geometry and Topology*,
vol. 1, Ed. Silvio Levy, Princeton University Press, 1997. (This is really
an expansion of a few chapters of Thurston's notes, but does not do much
on convex cocompactness/geometric finiteness.)
- Ratcliffe, John,
*Foundations of Hyperbolic Manifolds*,
Springer GTM.
- Bers, L,
*Simultaneous Uniformization*, Bull Amer. Math. Soc 66
(1960), 94-97
- Marden, A,
*The geometry of finitely generated Kleinian groups*,
Ann of Math (2) 99 )1974), 383-462
- Epstein, D.B.A. and Marden, A
*Convex hulls in hyperbolic space, a
theroem of Sullivan,
and measured pleated surfaces*, London Math. Soc. Lecture Note Ser.,
111, 1987
- Thurston, W.P.,Hyperbolic Structures on 3-manifolds II: Surface groups and 3-manifolds which
fiber over the circle, unpublished preprint (arxiv).
- Thurston, W.P.,Hyperbolic Structures on 3-manifolds I: Deformations of acylindrical
manifolds, Ann. of Math (1986).
- Bridson, M and Haefliger, A,
*Metric spaces of non-positive curvature*, Springer-Verlag (1999).
- Kent, R. and Leininger, C,
*Shadows of mapping class groups: capturing convex cocompactness*, GAFA (2008).

**Lecture Room and Times:** Tuesday, Thursday 2-3:20 in Engineering
Hall 106B6.

**Grades:** This is based on classroom attendence and
participation. I expect anyone who comes all semester to get an A (of
course, if you're sick you should stay home...). There will be no exams,
quizzes or homework collected.

**Problems:** I will assign problems and exercises throughout the
semester. There will be a wide range in the level of difficulty, from
completing proofs to open problems. I will have to be away a few times
this semester, and during that time, I'd like to have you go over problems
on those days.