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SOME REMARKS ON CONFIGURATION SPACES

By George Raptis and Communicated Brooke Shipley

Abstract

Abstract. This paper studies the homotopy type of the configuration spaces Fn(X) by introducing the idea of configuration spaces of maps. For every map f: X → Y, the configuration space Fn(f) is the space of configurations in X that have distinct images in Y. We show that the natural maps Fn(X) ← Fn(f) → Fn(Y) are homotopy equivalences when f is a proper cell-like map between d-manifolds. We also show that the best approximation to X ↦→ Fn(X) by a homotopy invariant functor is given by the n-fold product map. 1

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.2363
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