Vol. 44, No. 1, 1973

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The evaluation map and EHP sequences

George Edward Lang

Vol. 44 (1973), No. 1, 201–210

Let LB,X) be the space of maps from ΣB (the reduced suspension of B) to X with the compact-open topology, let lB X and LB,X;l) the path component of LB,X) containing l. For nice spaces the evaluation map ω; LB,X,l) X defined by ω(f) = f() is a fibration and gives rise to a long exact sequence in homotopy. The purpose of this paper is to show that the boundary map in that long exact sequence can be given by a generalized Whitehead product and that the sequence generalizes the EHP sequence of G. W. Whitehead.

Mathematical Subject Classification
Primary: 55E15
Secondary: 55E25
Received: 7 June 1971
Published: 1 January 1973
George Edward Lang