Symmetric ribbon disks

Aceto, Paolo (2014) Symmetric ribbon disks. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 23 (9). ISSN 0218-2165

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We study the ribbon disks that arise from a symmetric union presentation of a ribbon knot. A natural notion of symmetric ribbon number rS(K) is introduced and compared with the classical ribbon number r(K). We show that the difference rS(K) - r(K) can be arbitrarily large by constructing an infinite family of ribbon knots Kn such that r(Kn) = 2 and rS(Kn) > n. The proof is based on a particularly simple description of symmetric unions in terms of certain band diagrams which leads to an upper bound for the Heegaard genus of their branched double covers.

Item Type: Article
Additional Information: Cited By :1 Export Date: 23 September 2020 Correspondence Address: Aceto, P.; Dipartimento di Matematica, Universita di Firenze, Viale Morgagni, 67, Italy
Uncontrolled Keywords: symmetric union; ribbon number; Ribbon knot; Heegaard genus; branched cover;
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria
Depositing User: MTMT SWORD
Date Deposited: 24 Sep 2020 07:14
Last Modified: 24 Sep 2020 07:14

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