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The four-genus of connected sums of torus knots


Speaker: Cornelia Van Cott, University of San Francisco
Location: 2112 MSB
Start time: Tue, Oct 27 2015, 1:10PM

We consider the problem of finding surfaces of minimal genus in B^4 with boundary equal to the connected sum of torus knots. This problem arises naturally in the study of deformations of algebraic curves and in determining the minimal cobordism distance between torus knots. We will show that the classical Tristram-Levine signature function as well as the recently defined Upsilon function both provide some elegant answers to this problem. This is joint work with Chuck Livingston.