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
. (If
is a handlebody then
.) The positive boundary of C, denoted
, is
minus the negative boundary.
There is a dual construction of compression bodies starting with a surface and attaching 2-handles to
. In this case
is
, and
is
minus the positive boundary.
Compression bodies often arise when manipulating Heegaard splittings.