
Math
9071: Teichmuller and NielsenThurston Theory
Spring 2017
Meets:  Tue/Thu
2:00  3:200 in
Wachman Hall, room 1036 
Instructor:  David
Futer 
Office:  1026
Wachman Hall 
Office
Hours:  by
appointment 
Email:  dfuter
at
temple.edu 
Phone:  (215)
2047854 
Course content:
This course will focus on the symmetry groups of manifolds and cell
complexes. We will look at both the geometric and algebraic properties of the
mapping class group, which can roughly be thought of as the group of
symmetries of a surface. One of the ways in which we will study the group is
by designing a certain cell complex on which it acts by isometries. This
principle has wide generalizations: one can derive a great deal of information
about a group by constructing a geometric object for the group to act on.
In the spring semester, we will focus our attention on the braid groups, which
are a special class of mapping class groups. In particular, we will study the
representation theory of these groups, with connections to invariants of knots
and links.
Textbooks:
Prerequisites: Math 9120.
Grading: Grades will be assigned based on homework and a presentation
toward the end of the semester.
Detailed schedule
Day 
Topic 
Reading 
Homework/Note 
1/17  Residual finiteness 
P. 177181  See Alperin paper
 1/19  Torsion  P. 200203 
 1/24  Orbifold basics  P.203206 
 1/26  Geometric orbifolds; Hurwitz's theorem  P. 207210 
 1/31  Wyman's theorem; realizing finite groups  P.211214 
 2/2  DehnNielsenBaer theorem  P.219221, 236238 
 2/7  Braid groups  P. 239247 
 2/9  no class  
 2/14  Intro to Teichmuller space  P. 261267 
 2/16  Teichmuller space via lattices  P. 269272 
 2/21  Dimension counts; hexagons and pants  P. 272277 
 2/23  FenchelNielsen coordinates 
P. 278285  Homework 1, due 3/2
 3/2  Teichmuller geometry  P. 294298 
 3/7  Quasiconformal maps, measured foliations 
P. 299304 
 3/9  Singular measured foliations  P. 305308 
 3/21  Holomorphic quadratic differentials  P. 309313 
 3/23  The vector space of quadratic differentials 
P. 314318 
 3/28  Teichmuller maps  P. 319324 
 3/30  Grotzcsh's theorem; Teichmuller uniqueness  P. 325330 
 4/4  Teichmuller existence, geodesics  P. 331339 
 4/6  Moduli space; Fricke's theorem  P. 342351 
 4/11  Mumford's compactness criterion  P. 351357 
 4/13  Three types of mapping classes  P. 367369, 374376 
 4/18  Periodic mapping classes; reducing systems 
P. 370373 
 4/20  Collar lemma; parabolic implies reducible 
P. 380385  Homework 2, due 5/5
 4/25  Hyperbolic isometries are pseudoAnosov  P. 385388 
 4/27  Casson's criterion; lengths under iteration  P. 397400, 419422

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