Mathematics Colloquia and Seminars
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Boundaries of Teichmuller spaces and end-invariants for hyperbolic 3-manifolds.Geometry/Topology
|Speaker: ||Jeff Brock, Stanford University|
|Location: ||693 Kerr|
|Start time: ||Wed, May 5 1999, 4:10PM|
In two celebrated boundaries for Teichmuller space
due to Bers and Thurston geodesic laminations arise in natural ways:
An important conjecture of Thurston's is that E is an injection.
As a related issue, we will consider continuity properties of the
mapping E. We will show that E is discontinuous, but lower-semi
continuous in the quotient topologies. We formulate a topology
(the end-invariant topology) on the range in which E is continuous.
This topology predicts new data about limiting end-invariants
and reveals some fundamental obstructions to developing a complete
picture of how they vary.
- A point M in Bers' boundary, a hyperbolic 3-manifold has
an associated geodesic lamination that has been "pinched."
- A point L in Thurston's, a measured lamination up to scale,
records asymptotic stretching of divergent marked Riemann surfaces.
Such geodesic laminations provide a natural mapping from a quotient
of Bers boundary to a quotient of Thurston's, by assigning to
M its "end-invariant" E(M), the pinched geodesic lamination for M.