  A charged space is a space equipped with two distinct base points. Such
spaces arise as the unreduced suspension of an unbased space. More generally,
one can work in the fiberwise setting over a fixed space B. A fiberwise charged
space over B is a space X equipped with map to B and having two sections. One
can ask whether or not a fiberwise charged space over B is a fiberwise
suspension. We answer this question in a certain metastable range by producing
a necessary and sufficient obstruction. As an application we show how this can
be used to study when an embedding into a smooth manifold of the form N x I
compresses to an embedding into N .
