
Math
9024: Knot Theory and LowDimensional Topology
Fall 2014
Meets:  Tue/Thu
9:30 AM  10:50 AM in
Wachman Hall, room
1015D 
Instructor:  David
Futer 
Office:  1038
Wachman Hall 
Office
Hours:  by
appointment 
Email:  dfuter
at
temple.edu 
Phone:  (215)
2047854 
Course content:
This course will be a continuation of Math 9023. We will focus somewhat more
on the geometric side of knot theory and 3manifold theory. Some topics
include:
 Geometric topology of alternating knots
 Fibrations of 3manifolds over the circle
 NielsenThurston classification of mapping classes
 Geometric structures on 3manifolds
 Hyperbolic geometry
 Volume conjecture
Textbooks: We will draw material from the following sources, in
addition to miscellaneous articles.
Prerequisites: Math 9023 or permission of the instructor.
Grading: Grades will be assigned based on homework and a presentation
toward the end of the semester.
Class Schedule and Homework
This table will be gradually filled in as the course progresses. The letters
H, L, P, and T stand for the above references. FM stands for FarbMargalit, CB
for CassonBleiler.
Day 
Topic 
Reference 
Homework 
1/13  Polyhedral decomposition for alternating knots  P, p. 914 
 1/15  Normal surfaces, incompressible surfaces  L, p. 3236 
 1/20  Surfaces in alternating knot complements  L, p. 3638 
 1/22  Basic hyperbolic geometry  P,
p. 1921  Homework 1, due 1/29
 1/29  Hyperbolic geometry  T,
p. 5364  Homework 2, due 2/5
 2/3  Hyperbolic surfaces  T, p. 4748, 8690. 
 2/5  Completeness of surfaces  P, p. 3439. T, p. 147150.
 Homework 3, due 2/12
 2/10  Hyperbolic 3manifolds, (G,X) structures  P, p. 2731. T,
p. 110115 
 2/12  Developing map, holonomy, completeness  P, p. 3234, 39. T, p. 139146. 
 2/17  Gluing equations for 3manifolds  P, p. 4548. 
 2/19  Gluing and completeness equations  P,
p. 4852.  Homework 4, due 2/26
 2/24  Mostow rigidity  BenedettiPetronio 
 2/26  Hyperbolic Dehn surgery  P,
p. 5661  Homework 5, do over the break
 3/10  Model geometries  T, p. 179189 
 3/12  Seifert fibrations,
orbifolds  Wikipedia
on SFS 
Homework 6, due 3/19
 3/17  Geometric orbifolds and
SFS  Orbifolds; Selberg's
lemma 
 3/19  Sphere and torus decomposition  H, p. 616 
 3/24  Geometrization
theorem  Wikipedia;
FM, p. 400401. 
 3/26  Measured foliations, pseudoAnosovs  FM,
p. 314320.  Homework 7, due 4/2
 3/31  NielsenThurston theorem; criteria for pseudoAnosovs  FM, p. 397399; 420423 
 4/2  Geodesic laminations  CB P. 6069 
 4/7  Constructing the stable lamination  CB, p. 7983 
 4/9  Unique stable & unstable laminations  CB, p. 8387 
 4/14  Stable & unstable foliations  CB, P. 8994 
 4/16  Transverse measures  CB, P. 95102 
 4/21  Presentation: Thomas  
 4/23  Presentation: Zach  
 4/28  Presentation: Will, Tim  
 4/30  Presentation: Geoff  

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