Title: Taut sutured handlebodies as twisted homology products
Abtract: We explore a method for certifying that a sutured manifold is taut, by showing that it is homologically simple - a so-called rational homology product. Most sutured manifolds do not have this form, but do always take the more general form of a twisted homology product, which incorporates a representation of the fundamental group. The question then becomes, how complicated of a representation is needed to realize a given sutured manifold as such?
Title: Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
Title: Taut foliations of compact 3-manifolds with constrained boundary slopes
Title: Persistently foliar knots
Title: Surface complexes of Seifert fibered spaces
Title: Genus 2 Heegaard splittings and Dehn surgery on tunnel number one knots
Abstract: We generalize a theorem of Homma, Ochiai, and Takahashi, and discuss its relation with the Berge conjecture.
Title: ADE links and cyclic branched covers
Abstract: The Dynkin diagrams of types A,D and E arise in many classification problems in mathematics. We conjecture a modest addition to this list: the fibered links that induce the standard tight contact structure on S3 and have some cyclic branched cover an L-space. We will discuss progress towards a proof of this conjecture. This is joint work with Michel Boileau and Steve Boyer.