Filtering the fiber of the pinch map
Brayton Gray
brayton@uic.edu
This paper develops the similarity between the loops on an odd dimensional
sphere and the fiber F of the pinch map from an odd dimensional mod p^r
Moore space to the sphere, for p odd. In particular, a Hopf invariant map
is defined and there is an EHP sequence up to a factor which is the loops
on a bouquet of higher dimensiona Moore spaces. As a consequence we have
two technical results about the mysterious connecting map from the double
loops on the sphere to the loops on F.