The twisting number of a ribbon knot is bounded below by its doubly slice genus


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Date

2024-04-11

Publication Type

Working Paper

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yes

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Abstract

The twisting number of a ribbon knot $K$ is the minimal number of tangle replacements on the symmetry axis of $J \# -J$ for any knot $J$ that is required to produce a symmetric union diagram of $K$. We prove that the twisting number is bounded below by the doubly slice genus and produce examples of ribbon knots with arbitrarily high twisting number, addressing a problem of Tanaka. As an application, we determine hitherto unknown doubly slice genera of some knots with 12 crossings.

Publication status

published

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Pages / Article No.

2404.07619

Publisher

Cornell University

Event

Edition / version

v1

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Subject

Geometric Topology (math.GT); FOS: Mathematics; 57K10, 57K30, 57K40

Organisational unit

09672 - Feller, Peter (ehemalig) / Feller, Peter (former) check_circle

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