Markov theorem for transversal links
S. Yu. Orevkov, V. V. Shevchishin
TL;DR
This paper establishes a Markov-type theorem characterizing when two braids represent transversally isotopic links, using conjugations and positive Markov moves.
Contribution
It provides a complete characterization of transversal link isotopy via braid operations, extending classical Markov theorems to the transversal setting.
Findings
Two braids are transversally isotopic iff related by conjugations and positive Markov moves.
The result offers a new criterion for transversal link classification.
It bridges braid group operations with transversal link theory.
Abstract
It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research