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Title: Biquandle brackets and knotoids
Authors: Güğümcü, Neslihan
Nelson, Sam
Oyamaguchi, Natsumi
Izmir Institute of Technology
Claremont McKenna College
Shumei University
Keywords: Biquandle brackets
Quantum enhancements
Issue Date: 2021
Publisher: World Scientific Publishing
Abstract: Biquandle brackets are a type of quantum enhancement of the biquandle counting invariant for oriented knots and links, defined by a set of skein relations with coefficients which are functions of biquandle colors at a crossing. In this paper, we use biquandle brackets to enhance the biquandle counting matrix invariant defined by the first two authors in (N. Gügümcü and S. Nelson, Biquandle coloring invariants of knotoids, J. Knot Theory Ramif. 28(4) (2019) 1950029). We provide examples to illustrate the method of calculation and to show that the new invariants are stronger than the previous ones. As an application we show that the trace of the biquandle bracket matrix is an invariant of the virtual closure of a knotoid.
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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