Week 
Date of Tuesday 
Tuesday 
Thursday 
Lecture notes 
Comments/Mistakes/Questions 
2 
Oct. 12 
Introduction. Surfaces and curves. 
Intersection number. Simplical complexes. 
Tuesday
Thursday 
See Thursday lecture for correct definition of inessential and
peripheral. (The annulus, torus, Möbius band, and Klein bottle
all give special cases.) 
3 
Oct. 19 
Arc and curve complexes. Distance. The Farey graph. 
Annuli. Subsurface projection. 
Tuesday
Thursday 
The Farey graph has a unique threecoloring. 
4 
Oct. 26 
Disjoint, nested, overlapping subsurfaces. 
Behrstock's Lemma. Markings. 
Tuesday
Thursday 
Oriented edges of the Farey graph are markings of
S_{1,1}. What are the twist and flip moves? 
5 
Nov. 2 
The marking graph. Cocompactness. Finite stabilizers.
Elementary moves. Local finiteness. Connectedness. 
The marking graph is quasiisometric to MCG(S) equipped with
the word metric.  Tuesday Thursday 
A version of the ŠvarcMilnor
Lemma: Suppose that G is a group acting via isometries on a
locally finite, connected graph X with finite vertex stabilizers
and finite quotient. Then G is finitely generated and the orbit
map from G to X is a quasiisometry of the word metric with the
path metric. 
6 
Nov. 9 
Projection bounds. Distance estimates. Bounded geodesic
image theorem. 
Tight geodesics, definition and existence. 
Tuesday
Thursday 
Chris Leininger
has given a proof of the Bounded Geodesic Image Theorem following
Bowditch. 
7 
Nov. 16 
Footprints. Subordinacy. Hierarchies. 
Hierarchies exist. Sigma. Structure of Sigma. 
Tuesday
Thursday 
Do infinite geodesics exist in C(S)? Thursday's
lecture: M_k(n) should count unutilized domains only. 
8 
Nov. 23 
More Sigma. Time order. 
Point order. "Finish" structure of Sigma. 
Tuesday
Thursday 

9 
Nov. 30 
Discuss applications. Slices and slice order. 
Transition slices and elementary moves. Resolutions. 
Tuesday
Thursday 
In Thursday's lecture I need one more condition on
τ_{0}: the bottom pair is (g_{H},
v_{0}). 
10 
Dec. 7 
Forward/backward paths. Sigma projection. Large link. 
Finish proof of the distance estimate. Applications. 
Tuesday
Thursday 
