Bulletin of the Korean Mathematical Society (대한수학회보)

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AN ALTERNATIVE PROOF FOR THE MINIMALITY OF STRONGLY QUASI-POSITIVE FIBERED KNOTS IN THE RIBBON CONCORDANCE POSET

  • Keiji Tagami (Department of The Faculty of Economics Sciences Hiroshima Shudo University)
  • Received : 2023.06.23
  • Accepted : 2023.08.07
  • Published : 2024.05.31
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Abstract

Baker proved that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among fibered knots in the three-sphere. By applying Rapaport's conjecture, which has been solved by Kochloukova, we can check that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among all knots in the three-sphere. In this short note, we give an alternative proof for the fact by utilizing the knot Floer homology.

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Acknowledgement

The author was supported by JSPS KAKENHI Grant number JP22K13923.

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