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: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nigerian Society of Physical Sciences
2022-10-01
|
| Series: | Journal of Nigerian Society of Physical Sciences |
| Subjects: | |
| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/1051 |
| _version_ | 1811194405373083648 |
|---|---|
| author | Faik Mayah Nisreen Alokbi Ali Sabeeh Rasheed |
| author_facet | Faik Mayah Nisreen Alokbi Ali Sabeeh Rasheed |
| author_sort | Faik Mayah |
| collection | DOAJ |
| description |
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 $\mathbb{R}^3\backslash \mathcal{B}_4$.
|
| first_indexed | 2024-04-12T00:26:33Z |
| format | Article |
| id | doaj.art-6d3216af8d8b4145825274fdd8c8f235 |
| institution | Directory Open Access Journal |
| issn | 2714-2817 2714-4704 |
| language | English |
| last_indexed | 2024-04-12T00:26:33Z |
| publishDate | 2022-10-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj.art-6d3216af8d8b4145825274fdd8c8f2352022-12-22T03:55:29ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042022-10-014410.46481/jnsps.2022.1051New Invariant Quantity To Measure The Entanglement In The BraidsFaik Mayah0Nisreen Alokbi1Ali Sabeeh Rasheed2Department of Software, College of Computer Science and IT, Wasit University, Wasit, IraqDepartment of Physics, College of Science, Wasit University, Wasit, IraqMinistry of Higher Education & Scientific Research, Baghdad, Iraq 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 $\mathbb{R}^3\backslash \mathcal{B}_4$. https://journal.nsps.org.ng/index.php/jnsps/article/view/1051LinkingnumberSato-LevineinvariantEvans-BergerformulaMagnetichelicity |
| spellingShingle | Faik Mayah Nisreen Alokbi Ali Sabeeh Rasheed New Invariant Quantity To Measure The Entanglement In The Braids Journal of Nigerian Society of Physical Sciences Linkingnumber Sato-Levineinvariant Evans-Bergerformula Magnetichelicity |
| title | New Invariant Quantity To Measure The Entanglement In The Braids |
| title_full | New Invariant Quantity To Measure The Entanglement In The Braids |
| title_fullStr | New Invariant Quantity To Measure The Entanglement In The Braids |
| title_full_unstemmed | New Invariant Quantity To Measure The Entanglement In The Braids |
| title_short | New Invariant Quantity To Measure The Entanglement In The Braids |
| title_sort | new invariant quantity to measure the entanglement in the braids |
| topic | Linkingnumber Sato-Levineinvariant Evans-Bergerformula Magnetichelicity |
| url | https://journal.nsps.org.ng/index.php/jnsps/article/view/1051 |
| work_keys_str_mv | AT faikmayah newinvariantquantitytomeasuretheentanglementinthebraids AT nisreenalokbi newinvariantquantitytomeasuretheentanglementinthebraids AT alisabeehrasheed newinvariantquantitytomeasuretheentanglementinthebraids |