2009 Topology Seminar - 03

For any positive integer n and any space X, Sub{n}(X) denotes the space of all finite subsets of X of cardinality at most n. This is almost like a configuration space but not quite. It appears in various contexts in algebraic and differential geometry. We review in this talk some known (and attractive) results due to Borsuk, Bott or more recently Tuffley. Then we build on this to give more detailed results on the connectivity of Sub{n}X for general X and on the top homology group when X is a manifold. This is joint work with Denis Sjerve (UBC).