The evaluation map and EHP sequences

George Edward Lang

Vol. 44 (1973), No. 1, 201–210

DOI: 10.2140/pjm.1973.44.201

Abstract

Let L(ΣB,X) be the space of maps from ΣB (the reduced suspension of B) to X with the compact-open topology, let l;ΣB → X and L(ΣB,X;l) the path component of L(ΣB,X) containing l. For nice spaces the evaluation map ω; L(ΣB,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

Milestones

Received: 7 June 1971

Published: 1 January 1973