Mathematics Colloquia and Seminars

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In 2022, Dai, Kang, Mallick, Park, and Stoffregen proved that the (2,1)-cable of the figure eight knot is not smoothly slice via an obstruction arising from the involutive Heegaard Floer homology of its double branched cover. This ruled out arguably the simplest candidate for a counterexample to the Slice-Ribbon Conjecture. In this talk I will give an alternate proof of that the (2,1)-cable of the figure eight knot is not smoothly slice which goes through Seiberg-Witten theory by way of Furuta's 10/8 Theorem and a strengthening of the 10/8 theorem by J. Bryan from 1997. The new obstruction arises from lower bounds on the genus of some surfaces embedded in nontrivial 4-manifolds. This work is joint with P. Aceto, M. Miller, J. Park, and A. Stipsicz.