Subject: question
From: Martin.A.Arkowitz@Dartmouth.EDU (Martin A. Arkowitz)
Date: 16 Oct 2005 18:24:16 EDT

Let Z be the mapping cone of a map X-->Y. Then there is 
the Barratt-Puppe sequence X-->Y-->Z-->Sigma(X)-->... 
and an operation of [Sigma(X),V] on [Z,V] for any space V. 
Apart from certain obvious situations (eg, V an H-space or f 
the inclusion of X in the cone on X), does anyone know of 
concrete calculations of the operation in specific cases? 
For instance, what is the orbit or stability group of a 
non-trivial element in [Z,V]?