| 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 three-coloring. |
| 4 |
Oct. 26 |
Disjoint, nested, overlapping subsurfaces. |
Behrstock's Lemma. Markings. |
Tuesday
Thursday |
Oriented edges of the Farey graph are markings of
S1,1. 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 quasi-isometric to MCG(S) equipped with
the word metric. | Tuesday Thursday |
A version of the Švarc-Milnor
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 quasi-isometry 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
τ0: the bottom pair is (gH,
v0). |
| 10 |
Dec. 7 |
Forward/backward paths. Sigma projection. Large link. |
Finish proof of the distance estimate. Applications. |
Tuesday
Thursday |
|
