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Title:
Topology Seminar Series - Speaker Matt Hedden
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Abstract:
Modulo a 4-dimensional equivalence relation, the set of knots in the 3-sphere can be endowed with a group structure. The resulting group is called the concordance group and, perhaps surprisingly, the group depends on whether we work with homeomorphisms or diffeomorphisms. Particularly important to understanding this distinction is the set of topologically slice knots: those knots which bound topologically flat embedded disks in the 4-ball. These knots generate a fundamental subgroup of the smooth concordance group of knots which, for instance, can be used to demonstrate the existence of a 4-manifold which is homeomorphic, but not diffeomorphic, to euclidean 4-space. I'll give an introduction and overview of the concordance groups, and discuss recent work which provides the first examples of (two-) torsion elements in this topologically slice subgroup. The new results which I'll mention are joint work with Se-Goo Kim and Charles Livingston.Related Papers:
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