The groups Gk+1k and fundamental groups of configuration spaces

DOI10.1142/9789811215476_0017zbMATH Open1448.57008arXiv1803.01195OpenAlexW3006984096MaRDI QIDQ5137285

V. O. Manturov

Publication date: 2 December 2020

Published in: New Trends in Algebras and Combinatorics (Search for Journal in Brave)

Abstract: In cite{HigherGnk}, the author has constructed natural maps from fundamental groups of topological spaces (restricted configuration spaces) to the groups $G_n^k$. In the present paper, we show that in the case of $n=k+1$, the group $G_{k+1}^k$ is isomorphic to the fundamental group of some (quotient space of) some configuration space. In particular, this leads to the solution of word and conjugacy problems in $G_4^3$ and sheds light on $G_{k+1}^k$ for higher $k$.

Full work available at URL: https://arxiv.org/abs/1803.01195

zbMATH Keywords

configuration spaceword problemgroupconjugacy problembraid

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Fundamental group, presentations, free differential calculus (57M05) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Knot theory (57K10)

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