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Biquandle Power Brackets

Neslihan Gügümcü, Sam Nelson

Abstract

In this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-cocycle invariants as special cases. Biquandle power brackets are generalizations of biquandle brackets in which the values of Kauffman states also depend on the biquandle colors they admit. We provide example computations and discuss the relationship between these new invariants and the previous cases.

Biquandle Power Brackets

Abstract

In this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-cocycle invariants as special cases. Biquandle power brackets are generalizations of biquandle brackets in which the values of Kauffman states also depend on the biquandle colors they admit. We provide example computations and discuss the relationship between these new invariants and the previous cases.
Paper Structure (5 sections, 4 theorems, 25 equations)

This paper contains 5 sections, 4 theorems, 25 equations.

Table of Contents

  1. Introduction
  2. Biquandle Basics
  3. Biquandle Power Brackets
  4. Examples
  5. Questions

Key Result

Theorem 1

The fundamental biquandle is an invariant of oriented links.

Theorems & Definitions (17)

  • Definition 1
  • Example 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • Remark 1
  • Theorem 2
  • Definition 4
  • Remark 2
  • Definition 5
  • ...and 7 more