New Invariant Quantity To Measure The Entanglement In The Braids

Faik Mayah, Nisreen Alokbi, Ali Sabeeh Rasheed
2022 Journal of the Nigerian Society of Physical Sciences  
In this work, we demonstrate that the integral formula for a generalised Sato-Levine invariant is consistent in certain situations with Evans and Berger's formula for the fourth-order winding number. Also, we found that, in principle, one can derive analogous high-order winding numbers by which one can calculate the entanglement of braids. The winding number for the Brunnian 4-braid is calculated algebraically using the cup product on the cohomology of a finite regular CW-space which is the complement $\mathbb{R}^3\backslash \mathcal{B}_4$.
doi:10.46481/jnsps.2022.1051 fatcat:sn2bfez5cvb7fdkessf7imwzde