Course Information for Math 595 GTG, Geometric Topology Spring 2016

  • Instructor information:
  • 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  • Thurston, W.P.,Hyperbolic Structures on 3-manifolds II: Surface groups and 3-manifolds which fiber over the circle, unpublished preprint (arxiv).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.