New Invariant Quantity To Measure The Entanglement In The Braids
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 wh...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nigerian Society of Physical Sciences
2022-10-01
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| Series: | Journal of Nigerian Society of Physical Sciences |
| Subjects: | |
| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/1051 |
| Summary: | 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 $\mathbb{R}^3\backslash \mathcal{B}_4$.
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| ISSN: | 2714-2817 2714-4704 |