Geodesic
Invariants of classical braids valued in $G_{n}^{2}$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 137-146.

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The aim of the present note is to enhance groups $G_{n}^{3}$ and to construct new invariants of classical braids. In particular, we construct invariants valued in $G_{N}^{2}$ groups. In groups $G_{n}^{2}$, the identity problem is solved; besides, their structure is much simpler than that of $G_{n}^{3}$. 
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     title = {Invariants of classical braids valued in $G_{n}^{2}$},
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V. O. Manturov. Invariants of classical braids valued in $G_{n}^{2}$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 137-146. http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a9/

[1] Manturov V. O., “O gruppakh $G_{n}^{2}$ i gruppakh Kokstera”, UMN, 72:2 (2017), 234–235

[2] Bardakov V. G., “The virtual and universal braids”, Fund. Math., 184 (2004), 1–18 | MR | Zbl

[3] Manturov V. O., Non-Reidemeister Knot Theory and Its Applications in Dynamical Systems, Geometry, and Topology, arXiv: 1501.05208

[4] Manturov V. O., “The groups $G_{n}^{k}$ and fundamental groups of configuration spaces”, J. Knot Theory Ramifications, 26 (2017) | MR

[5] Manturov V. O., Nikonov I. M., “On braids and groups $G_{n}^{k}$”, J. Knot Theory Ramifications, 24:13 (2015) | MR