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Title:
Fibered 3-manifolds and Weil-Petersson geometry
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Abstract:
When a 3-manifold fibers over the circle it often does so in infinitely many ways, and this gives a kind of laboratory for studying Teichmuller spaces and mapping class groups in many surfaces at once. Farb-Leininger-Margalit proved an influential theorem showing that fibered 3-manifolds organize the mapping classes of "short" Teichmuller translation length in all genera. We prove an analogous theorem for Weil-Petersson translation length. The proof uses recent theorems on renormalized volume as well as good old fashioned 3-manifold topology from the 1980s. Joint work with Leininger, Souto and Taylor.
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