Tohoku Mathematical Journal
2024
December
SECOND SERIES VOL. 76, NO. 4

Tohoku Math. J.
76 (2024), 541-560

Title A GENERALIZATION OF THE SLICE-RIBBON CONJECTURE FOR TWO-BRIDGE KNOTS AND $t_n$-MOVE

Author Tetsuya Abe and Keiji Tagami

(Received November 7, 2022, revised March 14, 2023)
Abstract. Daemi and Scaduto gave an extension of the slice-ribbon conjecture which asks whether a smooth concordance between a knot and a torus knot induces a ribbon concordance between them with an appropriate direction. In this paper, we characterize the two-bridge knots smoothly concordant to non-trivial torus knots via a local move called $t_n$-move. As an application, we confirm that Daemi and Scaduto's extension of the slice-ribbon conjecture is true for all two-bridge knots.

Mathematics Subject Classification. Primary 57K10.
Key words and phrases. Two-bridge knot, $t_n$-move, ribbon concordance

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