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.
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published
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2404.07619
Publisher
Cornell University
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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)