Grad Student Seminar in Geometric Group Theory: Spring 2010

MEETINGS: TBA, 7th Floor Grad Student Lounge, Hill Center, Busch Campus

Hyperbolic Polynomials & Cayley Graphs: 1, 2, 3
CAT(O) Geometry: 1, 2, 3
Amalgams and the Coset Graph
Thompson's Group F
Out (F_n) and Outer Space
Mapping Class Groups
Group Actions on Trees
Artin & Coxeter Groups
Bass-Serre Theory

-Braid Groups (Knight Fu): 1, 2, 3, 4, 5, 6, 7, 8, 9
-More CAT(O) Geometry (Dan Staley): 1, 2, 3
-Thurston Classification of Mapping Class Groups (Catherine Pfaff): 1, 2, 3
-Bass-Serre Theory & Kacs-Moody Groups (Leigh Cobbs): 1, 2, 3, 4, 5, 6
-Mapping Class Groups & Braid Groups (Knight Fu) 1, 2, 3, 4, 5, 6, 7, 8
-Mapping Class Groups (Catherine Pfaff): 1, 2
-Laminations, Singularities, Whitehead Graphs for Out(F_n): 1, 2, 3

(Thanks to Moon Duchin's Geometric Theory Seminar page for many of these references):

Out(F_n) and Outerspace:
-Lecture Notes from Out(F_n) Course: Lecture 1 , Lecture 2 , Lecture 3 , Lecture 4
- Automorphisms of Free Groups and Outer Space by Karen Vogtmann
-Bestvina, M.; Handel, M. Train tracks and automorphisms of free groups. Ann. of Math. (2) 135 (1992) no. 1, 1--51.
-Bestvina, M.; Handel, M. Train-tracks for surface homeomorphisms. Topology 34 (1995), no. 1, 109--140.
-Culler, M.; Vogtmann, K. Moduli of graphs and automorphisms of free groups. Invent. Math. 84 (1986), no. 1, 91--119. (pdf)

Main Sources for Coxeter Groups:
-Coxeter chapter from Angela Barnhill's thesis (pdf)
-Mike Davis's book (huge file) Of particular interest are Chapters 1,2,3,6,7,12.

Secondary Sources for Coxeter groups:
-Coxeter's 1934 paper "Discrete groups generated by reflections" (pdf)
-Humphrey's book Reflection groups and Coxeter groups
-Coxeter's book Regular polytopes

Some Recent Papers of Interest on Coxeter Groups and Related Topics :
-Sankaran Viswanath, "On growth types of quotients of Coxeter groups by parabolic subgroups" (arxiv)
-Angela Barnhill, "The FA_n conjecture for Coxeter groups" (arxiv)
-Daniel Allcock, "Infinitely many hyperbolic Coxeter groups through dimension 19" (pdf)
-Ruth Charney, "An introduction to right-angled Artin groups" (arxiv)

Sources for Bass-Serre Theory and Groups Acting on Trees:
-Scott-Wall, "Topological methods in group theory" (scanned pdf)
-Serre's Trees
-M.Davis's Appendix E on "Complexes of groups" (see link above, page 407)

Secondary Sources for Bass-Serre Theory and Groups Acting on Trees:
-Lubotzky's Tree lattices and lattices in Lie groups, in Combinatorial and Geometric Group Theory
-Bestvina, "R-trees in geometry, topology, and group theory" (ps)

Some Recent Papers of Interest on Bass-Serre Theory and Related Topics:
-Anne Thomas, "Lattices acting on right-angled buildings" (arxiv)
-Peter Shalen, "Three-manifold topology and the tree for PSL_2: The Smith conjecture and beyond" (dvi)
-Lisa Carbone, "Non-minimal Tree Actions and the Existence of Non-uniform Tree Lattices" (pdf)
-Benson Farb and Chris Hruska, Commensurability invariants for nonuniform tree lattices (pdf)

This seminar is organized by Catherine Pfaff cpfaff AT