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Floer homology and non-fibered knot detection

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Steven Sivek
Mon, 12/12/2022 - 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Please note the unusual starting time.

Hybrid.  Contact: Tobias Barthel, Viktoria Ozornova, Aru Ray and
Peter Teichner.

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.

File Non-fibered knot detection handout.pdf14.96 MB
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