Topology Seminar

Wednesday, March 2, 2016
4:15 PM - 5:30 PM (ET)
Exley Science Center Tower ESC 638
Event Type
Canalia, Caryn

Katherine Raous, Brandeis University: "Rational knots, Rational Seifert surfaces and genus bounds"

 Abstract: Let K be a knot in a 3-manifold Y that represents a torsion class in the first homology of Y. Since K is torsion, it has finite order, p, and unless p=1, K does not bound a surface in Y. However, we can always find a surface which wraps p times around K. Using this construction, Ni showed that K defines a filtration of the Heegaard Floer chain complex of Y indexed by the rationals. We will use this filtration to define analogues of the Ozsvath-Szabo tau-invariants for such knots and show that when Y bounds a rational homology ball, these invariants give a lower bound for the genus of a surface with boundary K.


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