||Date of Tuesday
||Introduction. Surfaces and curves.
||Intersection number. Simplical complexes.
||See Thursday lecture for correct definition of inessential and
peripheral. (The annulus, torus, Möbius band, and Klein bottle
all give special cases.)
||Arc and curve complexes. Distance. The Farey graph.
||Annuli. Subsurface projection.
||The Farey graph has a unique three-coloring.
||Disjoint, nested, overlapping subsurfaces.
||Behrstock's Lemma. Markings.
||Oriented edges of the Farey graph are markings of
S1,1. What are the twist and flip moves?
||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 varc-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
||Projection bounds. Distance estimates. Bounded geodesic
||Tight geodesics, definition and existence.
has given a proof of the Bounded Geodesic Image Theorem following
||Footprints. Subordinacy. Hierarchies.
||Hierarchies exist. Sigma. Structure of Sigma.
||Do infinite geodesics exist in C(S)?
lecture: M_k(n) should count unutilized domains only.
||More Sigma. Time order.
||Point order. "Finish" structure of Sigma.
||Discuss applications. Slices and slice order.
||Transition slices and elementary moves. Resolutions.
||In Thursday's lecture I need one more condition on
τ0: the bottom pair is (gH,
||Forward/backward paths. Sigma projection. Large link.
||Finish proof of the distance estimate. Applications.