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Topology/Geometry Seminar

Whitehead doubles, Conway tangles and rank-expansion

Abhishek Mallick (Rutgers University-New Brunswick)

Location:  Hill Center, Room 705
Date & time: Tuesday, 14 February 2023 at 4:00PM - 5:00PM

Hedden and Pinzón-Caicedo conjectured that every non-constant, winding number zero, satellite operation on the knot concordance group must admit an extreme form of rank-expansion, namely they map a rank-one subgroup to an infinite rank subgroup. In this talk, we will give the first known example of such a phenomenon by showing that the Whitehead doubles admit such a behavior, answering a question posed by Hedden and Pinzón-Caicedo. In fact, we will show that the conjecture holds for a larger class of satellite knots defined using Conway tangles. We will also recover many existing results on rank-conservation in the literature proved using gauge theoretic methods. Our primary tool is a surgery formula in Heegaard Floer homology proved by Hendricks-Hom-Stoffregen and Zemke. This is joint work with Irving Dai, Matt Hedden and Matt Stoffregen.

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