On combinatorial properties of a higher asymptotic ergodic invariant of magnetic lines

Tangled Magnetic Fields in Astro- and Plasma Physics; Quantised Flux in Tightly Knotted and Linked Systems

Akhmet'ev, P.M.^1

IZMIRAN, Troitsk, Moscow region, Russia^1

关键词: Asymptotic properties;    Combinatorial properties;    Ergodics;    Integral invariant;    Magnetic lines;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/544/1/012015/pdf
DOI  :  10.1088/1742-6596/544/1/012015

来源: IOP

【 摘 要 】

We investigate combinatorial properties of a higher invariant of magnetic lines, which is defined in the paper Akhmet'ev-1 (2013). Assume that a 3-component link L is modeled by a magnetic field B, which is represented by 3 closed magnetic lines. Main Theorem relates the integral invariant M(B) and a combinatorial invariant , defined from the Conway polynomial. As a corollary of Main Theorem, asymptotic properties for combinatorial links are proposed. The combinatorial invariant satisfies these asymptotic properties.