Cobordism Presentations
A handle presentation of a cobordism consists of a cobordism W where and an ascending union
where M is m-dimensional, W is m+1-dimensional, is diffeomorphic to and is obtained from by the attachment of i-handles. Whereas handle decompositions are the analogue for manifolds what cell decompositions are to topological spaces, handle presentations of cobordisms are to manifolds with boundary what relative cell decompositions are for pairs of spaces.
Read more about this topic: Handle Decomposition