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Groups acting on the circle with dense invariant laminations


Speaker: Harry Baik, UC Davis and Cornell University
Location: 2112 MSB
Start time: Tue, Mar 5 2013, 3:10PM

I propose a new way to look at the group actions on the circle via the number of transverse dense invariant laminations. As a motivational example, we characterize the Fuchsian groups in terms of the invariant laminations. Having infinitely many invariant laminations with some additional assumptions on the laminations guarantees that the given group is Fuchsian. From the ideas developed in the proof, we can also prove that having three invariant laminations with stronger assumptions gives the same result. The key ingredient is the convergence group theorem. The development of the theory was motivated by Thurston's universal circle construction for tautly foliated 3-manifold groups.