Homotopy groups of diagonal complements
Sadok Kallel, Inés Saihi · Algebraic & Geometric Topology · 2016
For X a connected finite simplicial complex we consider d .X; n/, the space of configurations of n ordered points of X such that no d C 1 of them are equal, and B d .X; n/, the analogous space of configurations of unordered points.These reduce to the standard configuration spaces of distinct points when d D 1.We describe the homotopy groups of d .X; n/ (resp.B d .X; n/) in terms of the homotopy (resp.homology) groups of X through a range which is generally sharp.It is noteworthy that the fundamental group of the configuration space B d .X; n/ abelianizes as soon as we allow points to collide, ie d 2. 55Q52; 55P10In memory of Abbas Bahri so greatly missed