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Topology of Stein Manifolds
by
Selman Akbulut
MSU / IAS
Compact Stein manifolds are nothing but Lefschetz fibrations over a disk with bounded fibers and positive monodromy (PALF's). The constructive proof this will be given.
The surjective map PALF's -> Compact Stein manifolds is not 1-1 (for example B^4 has a unique Stein structure while it has many PALF structures corresponding to fibered knots in S^3). So in a sense PALF's are `primitives' of Stein structures (as chain complexes are `primitives' of homology groups). We will use the underlying PALF structures to give canonical compactifications of Stein manifolds to closed symplectic manifolds (no boundary). Examples will be discussed.
Date received: May 15, 2002
Copyright © 2002 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cajk-03.