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.
In general, .
Reasons The reasons to introduce desuspension: Desuspension makes the category of spaces a triangulated category. If arbitrary coproducts were allowed, desuspension would result in all cohomology functors being representable.
See also Cone (topology) Equidimensionality Join (topology)
References
External links Desuspension at an Odd Prime When can you desuspend a homotopy cogroup?