Handlebody structures and splittings of simply-connected smooth 4-manifolds
by
Richard Stong
Rice University and University of California, San Diego

Suppose M is a closed, simply-connected smooth 4-manifold. Then M has a handlebody structure in which a subset of the 2-handles algebraically cancels the 1-handles and a disjoint subset of the 2-handles dually algebraically cancels the 3-handles. As a corollary one gets an improved version of the \Lambda-splitting theorem of M. Freedman and L. Taylor. If q_M = \lambda₁ \oplus\lambda₂ is any decomposition of the intersection form of M then there is a decomposition M = M₁ \cup _\Sigma M₂, where \Sigma is a homology 3-sphere, M₁ and M₂ are smooth and simply connected, and the intersection form of M_i is isomorphic to \lambda_i. Also one gets an improved version of the splitting theorem of Curtis-Freedman-Hsiang-Matveev-Stong. Suppose M₁ and M₂ are homeomorphic simply-connected smooth 4-manifolds. Then there are decompositions

Mi = N \cup \Sigma HDi ,

where \Sigma is a homology 3-sphere, N is smooth and simply-connected, and HD_i are smooth contractible 4-manifolds with boundary \Sigma.

Date received: January 31, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-34.