Casson towers and slice knots

Casson towers and slice knots

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Mark Powell, Université de Québec à Montreal (UQAM)
Fine Hall 314

A link is slice if it is the boundary of a disjoint union of flat discs in the 4-ball. The link slicing problem is closely related to the surgery and s-cobordism programme for classifying 4-manifolds. A Casson tower is a 4-manifold with boundary built from iteratively attempting to find an embedded disc in a 4-manifold using immersed discs. The number of iterated attempts is called the height of the Casson tower. I will describe results on obtaining embedded discs from Casson towers of height 4, 3 and 2, from joint work with Jae Choon Cha. The height 2 result in particular enabled us to construct an interesting class of new slice knots.