Department of Mathematics

Topology

  •  τ-invariants for knots in rational homology spheres
  •  09/11/2017
  •  4:10 PM - 5:30 PM
  •  C304 Wells Hall
  •  Katherine Raoux, MSU

Using the knot filtration on the Heegaard Floer chain complex, Ozsváth and Szabó defined an invariant of knots in the 3-sphere called τ(K). In particular, they showed that τ(K) is a lower bound for the 4-ball genus of K. Generalizing their construction, I will show that for a (not necessarily null-homologous) knot, K, in a rational homology sphere, Y, we can define a collection of τ-invariants, one for each spin-c structure on Y. In addition, these invariants give a lower bound for the genus of a surface with boundary K properly embedded in a negative definite 4-manifold with boundary Y.

 

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