Compression body

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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.


  • F.Bonahon, Geometric structures on 3-manifolds, Handbook of Geometric Topology, Daverman and Sher eds. North-Holland (2002).