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 3-manifolds de:Henkelkörper#Kompressionskörper