In the theory of 3-manifolds, a compression body is a kind of generalized handlebody.
A compression body is either a handlebody or the result of the following construction: Let
be a compression body.
The negative boundary of C, denoted
is a handlebody then
The positive boundary of C, denoted
minus the negative boundary.
There is a dual construction of compression bodies starting with a surface
minus the positive boundary.
Compression bodies often arise when manipulating Heegaard splittings.