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On an invariant of pure braids
- Authors: Manturov V.O.1,2, Nikonov I.M.1,2,3
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Affiliations:
- Moscow Institute of Physics and Technology
- Nosov Magnitogorsk State Technical University
- Lomonosov Moscow State University
- Issue: Vol 516 (2024)
- Pages: 79-82
- Section: MATHEMATICS
- URL: https://ruspoj.com/2686-9543/article/view/647965
- DOI: https://doi.org/10.31857/S2686954324020129
- EDN: https://elibrary.ru/XHVUPC
- ID: 647965
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Abstract
Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial.
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About the authors
V. O. Manturov
Moscow Institute of Physics and Technology; Nosov Magnitogorsk State Technical University
Author for correspondence.
Email: vomanturov@yandex.ru
Moscow Center for Fundamental and Applied Mathematics
Russian Federation, Moscow; MagnitogorskI. M. Nikonov
Moscow Institute of Physics and Technology; Nosov Magnitogorsk State Technical University; Lomonosov Moscow State University
Email: vomanturov@yandex.ru
Moscow Center for Fundamental and Applied Mathematics
Russian Federation, Moscow; Magnitogorsk; MoscowReferences
- Мантуров В.О. Теория узлов, М.–Ижевск: Институт компьютерных исследований, 2005.
- Artin E. Theory of Braids // Ann. Math. 1947. V. 48. N 1. P. 101–126.
- Manturov V.O., Fedoseev D., Kim S., Nikonov I. Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory. Series On Knots And Everything. V. 66. World Scientific, 2020.
- Manturov V.O., Nikonov I.M. On braids and groups Gkn // J. Knot Theory and Ramifications. 2015. V. 24. N 13. 1541009.
- Fortune S. Voronoi diagrams and Delaunay triangulations // Computing in Euclidean Geometry. Singapore: World Scientific Publishing Co, 1992. P. 193–233.
- Racah G. Theory of complex spectra II // Phys. Rev. 1942. V. 62. P. 438–462.
- Turaev, V.G., Viro O. Ya. State sum invariants of 3-manifolds and quantum 6j-symbols // Topology. 1992. V. 31. P. 865–902.
- Корепанов И.Г. SL(2)-решение уравнения пентагона и инварианты трехмерных многообразий // ТМФ. 2004. Т. 138. № 1. С. 23–34.
- Корепанов И.Г. Геометрия евклидовых тетраэдров и инварианты узлов // Фундамент. и прикл. матем. 2005. T. 11. № 4. С. 105–117.
- Manturov V.O., Fedoseev D., Kim S., Nikonov I. On groups Gkn and Гkn: A study of manifolds, dynamics, and invariants // Bull. Math. Soc. 2021. V. 11. N 2. 2150004.
- Penner R. The decorated Teichmuller space of punctured surfaces // Comm. Math. Phys. 1987. V. 113. N 2. 299–339.
- Kauffman L.H., Lins S. Temperley–Lieb Recoupling Theory and Invariants of 3-Manifolds. Princeton University Press, 1994.
- Тураев В.Г. Модули Конвея и Кауфмана полнотория // Зап. научн. сем. ЛОМИ. 1988. Т. 167. С. 79–89.
- Понарин Я.П. Элементарная геометрия. Т. 1. М.: МЦМНО, 2004.
- Birman J. Braids, Links, and Mapping Class Groups. Princeton University Press, 1974.
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