On an invariant of pure braids

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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.

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; Magnitogorsk

I. 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; Moscow

References

  1. Мантуров В.О. Теория узлов, М.–Ижевск: Институт компьютерных исследований, 2005.
  2. Artin E. Theory of Braids // Ann. Math. 1947. V. 48. N 1. P. 101–126.
  3. 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.
  4. Manturov V.O., Nikonov I.M. On braids and groups Gkn // J. Knot Theory and Ramifications. 2015. V. 24. N 13. 1541009.
  5. Fortune S. Voronoi diagrams and Delaunay triangulations // Computing in Euclidean Geometry. Singapore: World Scientific Publishing Co, 1992. P. 193–233.
  6. Racah G. Theory of complex spectra II // Phys. Rev. 1942. V. 62. P. 438–462.
  7. Turaev, V.G., Viro O. Ya. State sum invariants of 3-manifolds and quantum 6j-symbols // Topology. 1992. V. 31. P. 865–902.
  8. Корепанов И.Г. SL(2)-решение уравнения пентагона и инварианты трехмерных многообразий // ТМФ. 2004. Т. 138. № 1. С. 23–34.
  9. Корепанов И.Г. Геометрия евклидовых тетраэдров и инварианты узлов // Фундамент. и прикл. матем. 2005. T. 11. № 4. С. 105–117.
  10. 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.
  11. Penner R. The decorated Teichmuller space of punctured surfaces // Comm. Math. Phys. 1987. V. 113. N 2. 299–339.
  12. Kauffman L.H., Lins S. Temperley–Lieb Recoupling Theory and Invariants of 3-Manifolds. Princeton University Press, 1994.
  13. Тураев В.Г. Модули Конвея и Кауфмана полнотория // Зап. научн. сем. ЛОМИ. 1988. Т. 167. С. 79–89.
  14. Понарин Я.П. Элементарная геометрия. Т. 1. М.: МЦМНО, 2004.
  15. Birman J. Braids, Links, and Mapping Class Groups. Princeton University Press, 1974.

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