Towards a version of Markov's theorem for ribbon torus-links in\n \ℝ⁴

2017/06/28 by Céleste Damiani, Damiani, Celeste
Mathematics · #57Q45 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1706.09311

openalex publication_date 2017/06/28 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In classical knot theory, Markov's theorem gives a way of describing all\nbraids with isotopic closures as links in \ℝ³. We present a version\nof Markov's theorem for extended loop braids with closure in B³ \× S¹,\nas a first step towards a Markov's theorem for extended loop braids and ribbon\ntorus-links in \ℝ⁴.\n

Related

• Markov's theorem in 3--manifolds
• On Markov's Theorem
• Markov's Theorem
• A Markov's theorem for extended welded braids and links
• On a Map From Pure Braids to Knots