Abstract
In the paper [1], V. O. Manturov introduced the groups Gk n depending on two natural parameters n > k and naturally related to topology and to the theory of dynamical systems. The group G2 n , which is the simplest part of Gk n , is isomorphic to the group of pure free braids on n strands. In the present paper, we study the groups G2 n supplied with additional structures–parity and points; these groups are denoted by G2n,p and G2n,d. First,we define the groups G2n,p and G2n,d, then study the relationship between the groups G2 n , G2n,p, and G2n,d. Finally, we give an example of a braid on n + 1 strands, which is not the trivial braid on n + 1 strands, by using a braid on n strands with parity. After that, the author discusses links in S g × S1 that can determine diagrams with points; these points correspond to the factor S1 in the product S g × S1.
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Original Russian Text © Kim Seongjeong, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 4, pp. 549–567.
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Kim, S. The Groups G2 n with Additional Structures. Math Notes 103, 593–609 (2018). https://doi.org/10.1134/S0001434618030264
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DOI: https://doi.org/10.1134/S0001434618030264