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Connectivity of finite subset spaces
Geometry/Topology| Speaker: | Chris Tuffley, UC Davis |
| Location: | 693 Kerr |
| Start time: | Wed, Oct 1 2003, 4:10PM |
Description
The kth finite subset space of a topological space X is the space
exp_k(X) of non-empty subsets of X of size at most k, topologised as
a quotient of X^k. It can be thought of as a union of configuration
spaces of distinct unordered points in X, or as the quotient of
the symmetric product obtained by forgetting multiplicities. We'll
show that the kth finite subset space of a connected cell complex
is (k-2)-connected. This complements a result due to David Handel that
for path-connected Hausdorff X the map on pi_i induced by the inclusion
exp_k(X)-->exp_{2k+1}(X) is zero for all k and i.