The ν+-equivalence classes of genus one knots

The ν+-equivalence classes of genus one knots

The ν + -equivalence is an equivalence relation on the knot concordance group. This relation can be seen as a certain stable equivalence on knot Floer complexes C F K ∞ , and many concordance invariants derived from Heegaard Floer theory are invariant under the relation. In this paper, we show that...

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Veröffentlicht in:Selecta mathematica (Basel, Switzerland) Switzerland), 2023-09, Vol.29 (4), Article 63
1. Verfasser: Sato, Kouki
Format: Artikel
Sprache:eng
Schlagworte:
Equivalence
Invariants
Knot theory
Mathematics
Mathematics and Statistics
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Zusammenfassung:The ν + -equivalence is an equivalence relation on the knot concordance group. This relation can be seen as a certain stable equivalence on knot Floer complexes C F K ∞ , and many concordance invariants derived from Heegaard Floer theory are invariant under the relation. In this paper, we show that any genus one knot is ν + -equivalent to one of the trefoil, its mirror and the unknot.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-023-00867-6