Word and Conjugacy Problems in Groups G_k+1^k

2019/06/11 by D. A. Fedoseev, Fedoseev, Denis, А. Б. Карпов +3
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1906.04916

Abstract

Recently the third named author defined a 2-parametric family of groups G_n^k \citegnk. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups G_n^k and dynamical systems led to the discovery of the following fundamental principle: `If dynamical systems describing the motion of n particles possess a nice codimension one property governed by exactly k particles, then these dynamical systems admit a topological invariant valued in G_n^k'. The G_n^k groups have connections to different algebraic structures, Coxeter groups and Kirillov-Fomin algebras, to name just a few. Study of the G_n^k groups led to, in particular, the construction of invariants, valued in free products of cyclic groups. In the present paper we prove that word and conjugacy problems for certain G_k+1^k groups are algorithmically solvable, and the algorithms are constructive.

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