Course Information for Math 595 GTG, Geometric Topology
- 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
- 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,
- Bers, L, Simultaneous Uniformization, Bull Amer. Math. Soc 66
- 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.,
- 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fiber over the circle, unpublished preprint (arxiv).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
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.