The groups G_k+1^k and fundamental groups of configuration spaces

2018/03/03 by Manturov, Vassily Olegovich
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1803.01195

Abstract

In \citeHigherGnk, 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 G₄³ and sheds light on G_k+1^k for higher k.

Related

• The Groups G_n^k and Fundamental Groups of Configuration Spaces
• Word and Conjugacy Problems in Groups G_k+1^k
• On generalized configuration space and its homotopy groups
• The fundamental group and covering spaces
• Configuration spaces of commuting elements