Finite subset spaces of graphs and punctured surfaces

Details Finite subset spaces of graphs and punctured surfaces Finite subset spaces of graphs and punctured surfaces

2002-10-21

arxiv.org/abs/math/0210315v3

Algebr. Geom. Topol. 3 (2003) 873-904

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-29.abs.html

Scientific paper

The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X. We calculate the homology of the finite subset spaces of a connected graph Gamma, and study the maps (exp_k phi)_* induced by a map phi:Gamma -> Gamma' between two such graphs. By homotopy functoriality the results apply to punctured surfaces also. The braid group B_n may be regarded as the mapping class group of an n-punctured disc D_n, and as such it acts on H_*(exp_k D_n). We prove a structure theorem for this action, showing that the image of the pure braid group is nilpotent of class at most floor((n-1)/2).

Affiliated with

Also associated with

No associations

Rating

Finite subset spaces of graphs and punctured surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite subset spaces of graphs and punctured surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite subset spaces of graphs and punctured surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-355652