Satellite operators and knot concordance

Allison Miller (Swarthmore College)

Monday 11th October, 2021 16:00-17:00 Online


The classical satellite construction associates to any pattern P in a solid torus and companion knot K in the 3-sphere a satellite knot P(K), the image of P when the solid torus is ‘tied into’ the knot K. This operation descends to a well-defined map on the set of (smooth or topological) concordance classes of knots. Many natural questions about these maps remain open: when are they surjective, injective, or bijective? How do they behave with respect to measures of 4-dimensional complexity? How do they interact with additional group or metric space structure on the concordance set?

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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