Braid ordering and knot genus

2008/05/14 by Tetsuya Ito, Ito, Tetsuya · 1 citation
Computer Science · Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #math.GT #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0805.2042

10 pages, 6 figures, the main result is improved

openalex publication_date 2008/05/14 · arxiv created 2009/12/10 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The genus of knots is a one of the fundamental invariant and can be seen as a complexity of knots. In this paper, we give a lower bound of genus using Dehornoy floor, which is a measure of complexity of braids in terms of braid ordering.

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• Space of group orderings, quasi morphisms and bounded cohomology

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