Vol. 104, No. 1, 1983

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Bundles over configuration spaces

Frederick Ronald Cohen, Ralph Cohen, Nicholas J. Kuhn and Joseph Alvin Neisendorfer

Vol. 104 (1983), No. 1, 47–54

Let F(Rn,k) be the configuration space of ordered sets of k distinct points in Rn. F(Rn,k) is acted upon freely by the symmetric group on k letters, Σk. In this paper we calculate the order of the vector bundles

ξn,k : F(Rn,k )×Σk Rk → F(Rn, k)∕Σk.

Applications to the study of iterated loop spaces of spheres are also discussed.

Mathematical Subject Classification 2000
Primary: 55P35
Secondary: 55R50
Received: 7 July 1980
Published: 1 January 1983
Frederick Ronald Cohen
Ralph Cohen
Stanford University
United States
Nicholas J. Kuhn
Department of Mathematics
University of Virginia
Kerchof Hall PO Box 400137
Charlottesville VA 22904-4137
United States
Joseph Alvin Neisendorfer