Special Alternating Knots Are Band Prime

We prove that a special alternating knot does not decompose as a non-trivial band sum. This restricts concordances from special alternating knots, and we conjecture that special alternating knots are ribbon concordance minimal. We verify our conjecture in many cases. This work is motivated by anothe...

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Bibliographic Details
Published in:International mathematics research notices 2024-05, Vol.2024 (10), p.8758-8763
Main Authors: Boninger, Joe, Evan Greene, Joshua
Format: Article
Language:English
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Summary:We prove that a special alternating knot does not decompose as a non-trivial band sum. This restricts concordances from special alternating knots, and we conjecture that special alternating knots are ribbon concordance minimal. We verify our conjecture in many cases. This work is motivated by another conjecture of Owens and the second author, which posits that the set of alternating knots is downward closed under ribbon concordance.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnae009