Compression body explained

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 compact, closed surface (not necessarily connected). Attach 1-handles to along .

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.

References

• Book: Bonahon, Francis. Robert Daverman. Geometric structures on 3-manifolds. 93–164. Handbook of Geometric Topology. Daverman . Robert J.. Sher . Richard B.. . 2002. 1886669.