Tue, 05/21/2019 - 3:43pm
Title: TBA Abstract: TBA
Tue, 05/21/2019 - 3:42pm
  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…
Tue, 05/21/2019 - 3:41pm
  Title: Taut Foliations, Positive 3-Braids, and the L-Space Conjecture Abstract: The L-Space Conjecture is taking the low-dimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold Y. In particular, it predicts a 3-manifold Y isn’t ”simple” from the perspective of Heegaard-Floer homology if and only if Y admits a taut foliation. The reverse…
Tue, 05/21/2019 - 3:40pm
  Title: Taut foliations of compact 3-manifolds with constrained boundary slopes Abstract: A codimension one foliation of a 3-manifold is called taut if there exists a simple closed curve in the manifold that intersects each leaf of the foliation transversally. A surface bundle over a circle is a simple example of a 3-manifold with a taut foliation. Every compact 3-manifold can be obtained from such a surface bundle by Dehn filling the boundary…
Tue, 05/21/2019 - 3:39pm
  Title: Persistently foliar knots Abstract: A manifold with Heegard-Floer homology of minimal rank is called an L-space, since this is the case for lens spaces and other elliptic manifolds. A taut co-orientable foliation is associated with non-trivial elements of Heegard-Floer homology (by combined results of Eliashberg-Thurston, Ozsv´ath-Szab´o, Kazez-Roberts); hence, if a 3- manifold admits a taut, co-oriented foliation, it is not an L-space…
Tue, 05/21/2019 - 3:38pm
  Title: Surface complexes of Seifert fibered spaces Abstract: Curve complexes of surfaces provide information about surfaces and 3-manifolds in a variety of ways. Building on the success of curve complexes, we define surface complexes for 3-manifolds. The surface complex naturally decomposes into subcomplexes called Kakimizu complexes. For Seifert fibered spaces the relation between the surface complex and its subcomplexes can be described…
Tue, 05/21/2019 - 3:37pm
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.
Tue, 05/21/2019 - 3:35pm
Title: TBA Abstract: TBA
Tue, 05/21/2019 - 3:32pm
  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.
Tue, 05/21/2019 - 3:31pm
Title : Cyclic branched covers and the L-space conjecture Abstract : We survey what is known about the L-space conjecture for manifolds obtained as cyclic branched covers of links in the 3-sphere and report, in particular, on joint work with Michel Boileau and Cameron Gordon and with Ying Hu.