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Knot concordance and 4-manifolds

Frontiers in Mathematics Colloquium Lisa Piccirillo
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Wednesday, October 23, 2019
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3:15 pm - 4:15 pm
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Lisa Piccirillo (University of Texas at Austin)
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Frontiers In Mathematics Colloquium

There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will highlight some historical and recent connections between knot concordance (a weak notion of equivalence for knots) and the study of 4-manifolds, with a particular emphasis on applications of knot concordance to the construction and detection of small 4-manifolds which admit multiple smooth structures. I will also discuss a new method for using 4-manifolds to study knot concordance, and use it to show that the Conway knot is not slice.

Reception to follow at 4:30.