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Floer Homology and Non-Fibered Knot Detection

[HYBRID WORKSHOP] Floer Homotopical Methods in Low Dimensional and Symplectic Topology November 14, 2022 - November 18, 2022

November 14, 2022 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Steven Sivek (Max-Planck-Institut für Mathematik; Imperial College, London)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Floer Homology And Non-Fibered Knot Detection

Abstract

Floer homology can tell whether a knot is fibered, and this has led to proofs that both knot Floer homology and Khovanov homology can positively identify a small handful of knots: the unknot, the trefoils, the figure eight, and the cinquefoil. In this talk, I'll discuss recent work with John Baldwin in which we show for the first time that both invariants can also detect non-fibered knots, including 5_2, and that HOMFLY homology detects infinitely many knots. The key input is a classification of genus-1 knots which are "nearly fibered" from the perspective of knot Floer homology.

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Floer Homology And Non-Fibered Knot Detection

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