Partially Multiplicative Biquandles and Handlebody-Knots

2016/02/18 by Atsushi Ishii, Ishii, Atsushi, Sam Nelson +1
Computer Science · Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1602.05865

openalex publication_date 2016/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce several algebraic structures related to handlebody-knots, including G-families of biquandles, partially multiplicative biquandles and group decomposable biquandles. These structures can be used to color the semiarcs in Y-oriented spatial trivalent graph diagrams representing S¹-oriented handlebody-knots to obtain computable invariants for handlebody-knots and handlebody-links. In the case of G-families of biquandles, we enhance the counting invariant using the group G to obtain a polynomial invariant of handlebody-knots.

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