Bundles over configuration spaces

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

Vol. 104 (1983), No. 1, 47–54

DOI: 10.2140/pjm.1983.104.47

Abstract

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, Σ_k. In this paper we calculate the order of the vector bundles

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

Mathematical Subject Classification 2000

Primary: 55P35

Secondary: 55R50

Milestones

Received: 7 July 1980

Published: 1 January 1983