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Tag Archives: 3manifolds
3manifolds everywhere
When I started in graduate school, I was very interested in 3manifolds, especially Thurston’s geometrization conjecture. Somehow in dimension 3, there is a marvelous marriage of flexibility and rigidity: generic 3manifolds are flexible enough to admit hyperbolic structures — i.e. Riemannian metrics … Continue reading
Posted in 3manifolds, Groups, Hyperbolic geometry
Tagged 3manifolds, acylindrical, quasiconvex group, Random groups, Sierpinski carpet
9 Comments
Agol’s Virtual Haken Theorem (part 1)
I am in Paris attending a workshop at the IHP where Ian Agol has just given the first of three talks outlining his proof of the Virtual Haken Conjecture and Virtual Fibration Conjecture in 3manifold topology (hat tip to Henry … Continue reading
The topological CauchySchwarz inequality
I recently made the final edits to my paper “Positivity of the universal pairing in 3 dimensions”, written jointly with Mike Freedman and Kevin Walker, to appear in Jour. AMS. This paper is inspired by questions that arise in the … Continue reading
Posted in 3manifolds, TQFT
Tagged 3manifolds, BessonCourtoisGallot, compression body, DijkgraafWitten, Hamilton, hyperbolic manifolds, JSJ decomposition, Miles Simon, minimal surface, Perelman, Ricci flow, scalar curvature, TQFT, unitary, universal pairing, volume entropy, volume inequality
3 Comments