A bound on the complexity of the JSJ decomposition of 3-manifolds with boundary.

We show approximately that the number of components in the JSJ decomposition of a compact, orientable, irreducible 3-manifold with incompressible boundary is bounded by a function of the Heegaard genus and the Euler characteristic of the boundary. This extends a result of Scharlemann and Schultens on closed, orientable, irreducible 3-manifolds. Using Scharlemann and Schulten's measure I (V) of complexity for a Seifert fibre space V, we show that the complexity of certain Seifert fibred components of the JSJ decomposition is also bounded by a function of the Heegaard genus and Euler characteristic of the boundary of the 3-manifold.PhDMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126873/2/3276346.pd