Department of Mathematics

Geometry and Topology

  •  Yi Ni, Caltech
  •  Thurston norm minimizing Seifert surfaces
  •  09/08/2020
  •  3:00 PM - 4:00 PM
  •  Online (virtual meeting)

Let K be a null-homologous knot in a closed 3-manifold Y, and F be a Seifert surface. One can cap off the boundary of F with a disk in the zero surgery on K to get a closed surface F_0. If we know that F is Thurston norm minimizing, we can ask whether F_0 is also Thurston norm minimizing. A classical theorem of Gabai says that the answer is Yes when Y is the 3-sphere. Gabai's theorem can be generalized to many other 3-manifolds using Heegaard Floer homology. In this talk, we will discuss a sufficient condition for F_0 to be Thurston norm minimizing which relates this property to the 4-genus of the knot. Zoom:



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