Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 3, Number 2 (2003), 873-904.
Finite subset spaces of graphs and punctured surfaces
The th finite subset space of a topological space is the space of non-empty finite subsets of of size at most , topologised as a quotient of . The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in . We calculate the homology of the finite subset spaces of a connected graph , and study the maps induced by a map between two such graphs. By homotopy functoriality the results apply to punctured surfaces also. The braid group may be regarded as the mapping class group of an –punctured disc , and as such it acts on . We prove a structure theorem for this action, showing that the image of the pure braid group is nilpotent of class at most .
Algebr. Geom. Topol., Volume 3, Number 2 (2003), 873-904.
Received: 21 February 2003
Revised: 16 September 2003
Accepted: 23 September 2003
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 54B20: Hyperspaces
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 20F36: Braid groups; Artin groups 55Q52: Homotopy groups of special spaces
Tuffley, Christopher. Finite subset spaces of graphs and punctured surfaces. Algebr. Geom. Topol. 3 (2003), no. 2, 873--904. doi:10.2140/agt.2003.3.873. https://projecteuclid.org/euclid.agt/1513882420