
Math
9510: Hyperbolic 3Manifolds
Fall 2022
Meets:  Tue/Thu
11:0012:20 in
Wachman Hall, room 617 
Instructor:  David
Futer 
Office:  1026
Wachman Hall 
Office
Hours:  Tue 3:004:30, Thu 9:3011:00, or by
appointment 
Email:  dfuter
at
temple.edu 
Phone:  (215)
2047854 
Course content:
Continuing the theme from Math 9500, this course aims to describe a moderately
detailed picture of hyperbolic 3manifolds. We will begin with knots and
links in the 3sphere, 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 thickthin
decomposition, and Mostow rigidity.
References:
Prerequisites: Math 806162.
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 figure8 knot  Purcell, Chapter
1 
 1/19  Hyperbolic structure on the figure8 knot  Martelli, p. 446447 
 1/24  Hyperbolic structure on the Whitehead link  
 1/26  Gluing and completeness for surfaces  Purcell, p. 5459
 Homework 1, due Thursday 2/2
 1/31  Edge gluing equations for 3manifolds  Purcell,
p. 6973 
 2/2  Developing map and holonomy; completeness equations 
Purcell, 5053; p. 7476 
 2/7  Worksheet  
 2/9  Worksheet  
 2/14  Elementary subgroups; thick & thin parts  Purcell,
p. 8892 
 2/16  The Margulis lemma  Martelli, p. 116119; Purcell,
p. 95101 
 2/21  Thickthink decomposition in finite volume  Martelli,
p. 119122 
 2/23  Length spectra and isometry groups  Martelli,
p. 123125 
 2/28  No class  
 3/2  Isometry groups, residual finiteness  Martelli,
p. 126128 
 3/14  Limit sets, convex cores  Martelli, p. 135137 
 3/16  Limit sets and domains of discontinuity  Martelli,
p. 137138; animations 
 3/21  Quasiisometries and pseudoisometries  Martelli, p. 143144 
 3/23  Extending pseudoisometries to the boundary  Martelli,
p. 145147 
 3/28  Extending pseudoisometries to the boundary  Martelli,
p. 148150 
 3/30  Volumes of simplices  Martelli, p. 405409 

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Last modified: Fri Aug 21 13:41:22 PDT 2009
