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Acknowledgments

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The authors would like to express their heartfelt gratitude to L. A Bokut’, H. Boden, J. S. Carter, A. T. Fomenko, S. G. Gukov, Y. Han, D. P. Ilyutko, A. B. Karpov, R. M. Kashaev, L. H. Kauffman, M. G. Khovanov, A. A. Klyachko, P. S. Kolesnikov, I. G. Korepanov, S. V. Matveev, A. Yu. Olshanskii, W. Rushworth, G. I. Sharygin, V. A. Vassiliev, Zheyan Wan, Jun Wang, J. Wu and Zerui Zhang for their interest and various useful discussions on the present work. We are grateful to Efim I. Zelmanov for pointing out the resemblance between the groups and Kirillov–Fomin algebras.

The first named author would like to express his special thanks to (11 Sep. 1952–4 Sep. 2019):

I learnt a lot about word problems and conjugacy problems in the braid group from him. Meeting him many times during the last twenty years increased my knowledge in braid group theory. It is a great loss for the mathematical community that he passed away in 2019.”

— Vassily Olegovich Manturov

The first named author was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (grant No. 14.Y26.31.0025 of the government of the Russian Federation). The second named author was supported by the program “Leading Scientific Schools” (grant no. NSh-6399.2018.1, Agreement No. 075-02-2018-867) and by the Russian Foundation for Basic Research (grant No. 19-01-00775-a). The fourth named author was supported by the program “Leading Scientific Schools” (grant no. NSh-6399.2018.1, Agreement No. 075-02-2018-867) and by the Russian Foundation for Basic Research (grant No. 18-01-00398-a).

Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory

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