Desuspension


In topology, a field within mathematics, desuspension is an operation inverse to suspension.

Definition

In general, given an n-dimensional space, the suspension has dimension n + 1. Thus, the operation of suspension creates a way of moving up in dimension. In the 1950s, to define a way of moving down, mathematicians introduced an inverse operation, called desuspension. Therefore, given an n-dimensional space, the desuspension has dimension n – 1.
Note that in general.

Reasons

The reasons to introduce desuspension:
  1. Desuspension makes the category of spaces a triangulated category.
  2. If arbitrary coproducts were allowed, desuspension would result in all cohomology functors being representable.