Desuspension

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

In general, given an n-dimensional space ${\displaystyle X}$, the suspension ${\displaystyle \Sigma {X}}$ 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 ${\displaystyle \Sigma ^{-1}}$, called desuspension. Therefore, given an n-dimensional space ${\displaystyle X}$, the desuspension ${\displaystyle \Sigma ^{-1}{X}}$ has dimension n – 1.

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