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
S be a compact, closed surface (not necessarily connected). Attach 1-handles to
S × [ 0 , 1 ] along
S × { 1 } .
Let C be a compression body. The negative boundary of C, denoted ∂ − C , is S × { 0 } . (If C is a handlebody then ∂ − C = ∅ .) The positive boundary of C, denoted ∂ + C , is ∂ C minus the negative boundary.
There is a dual construction of compression bodies starting with a surface S and attaching 2-handles to S × { 0 } . In this case ∂ + C is S × { 1 } , and ∂ − C is ∂ C minus the positive boundary.
Compression bodies often arise when manipulating Heegaard splittings.
