Uniqueness of reduced alternating rational 3-tangles

2014/01/28 by Kwon, Bo-hyun
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1401.7259

Abstract

In this paper, We introduce an invariant of rational n-tangles which is obtained from the Kauffman bracket. It forms a vector with Laurent polynomial entries. We prove that the invariant classifies the rational 2-tangles and the reduced alternating rational 3-tangles. We conjecture that it classifies the rational 3-tangles as well.

Related

• On the classification of rational tangles
• On the classification of a large set of rational 3-tangle diagrams
• A Bridge between Conway-Coxeter Friezes and Rational Tangles through the Kauffman Bracket Polynomials
• On detecting the trivial rational 3-tangle
• A classification of rational 3-tangles