## Math 9510: Hyperbolic 3-Manifolds

### Fall 2022

 Meets: Tue/Thu 11:00-12:20 in Wachman Hall, room 617 Instructor: David Futer Office: 1026 Wachman Hall Office Hours: Tue 3:00-4:30, Thu 9:30-11:00, or by appointment E-mail: dfuter at temple.edu Phone: (215) 204-7854

Course content: Continuing the theme from Math 9500, this course aims to describe a moderately detailed picture of hyperbolic 3-manifolds. We will begin with knots and links in the 3-sphere, and construct hyperbolic structures on their complements. We will then go through some structural results in the theory: completeness and incompleteness of geometric structures, the thick-thin decomposition, and Mostow rigidity.

References:

Prerequisites: Math 8061-62.

Grading: Grades will be assigned based on homework and a presentation toward the end of the semester.

### Detailed schedule

This will be gradually filled in as the semester progresses.
Day Topic Reading Homework/Note
1/17 Motivating example: the figure-8 knot Purcell, Chapter 1
1/19 Hyperbolic structure on the figure-8 knot Martelli, p. 446-447
1/24 Hyperbolic structure on the Whitehead link
1/26 Gluing and completeness for surfaces Purcell, p. 54-59 Homework 1, due Thursday 2/2
1/31 Edge gluing equations for 3-manifolds Purcell, p. 69-73
2/2 Developing map and holonomy; completeness equations Purcell, 50-53; p. 74-76
2/7 Worksheet
2/9 Worksheet
2/14 Elementary subgroups; thick & thin parts Purcell, p. 88-92
2/16 The Margulis lemma Martelli, p. 116-119; Purcell, p. 95-101
2/21 Thick-think decomposition in finite volume Martelli, p. 119-122
2/23 Length spectra and isometry groups Martelli, p. 123-125
2/28 No class
3/2 Isometry groups, residual finiteness Martelli, p. 126-128
3/14 Limit sets, convex cores Martelli, p. 135-137
3/16 Limit sets and domains of discontinuity Martelli, p. 137-138; animations
3/21 Quasi-isometries and pseudo-isometries Martelli, p. 143-144
3/23 Extending pseudo-isometries to the boundary Martelli, p. 145-147
3/28 Extending pseudo-isometries to the boundary Martelli, p. 148-150
3/30 Volumes of simplices Martelli, p. 405-409

[Home] [Research] [Teaching] [News] [Personal] [Photos]

dfuter at temple edu
Last modified: Fri Aug 21 13:41:22 PDT 2009