Minimum Braids: A Complete Invariant of Knots and Links

2004/01/06 by Thomas A. Gittings, Gittings, Thomas A.
Computer Science · Mathematics · #57M15 #57M27 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.AT #math.GT #msc:57M15 #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0401051

40 pages

arxiv created 2004/01/06 · openalex publication_date 2004/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Minimum braids are a complete invariant of knots and links. This paper defines minimum braids, describes how they can be generated, presents tables for knots up to ten crossings and oriented links up to nine crossings, and uses minimum braids to study graph trees, amphicheirality, unknotting numbers, and periodic tables.

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