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Abstract
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The topology of broken
Lefschetz fibrations is studied by means of handle decompositions. We consider a
slight generalization of round handles and describe the handle diagrams for all that
appear in dimension four. We establish simplified handlebody and monodromy
representations for a certain subclass of broken Lefschetz fibrations and pencils,
showing that all near-symplectic closed 4-manifolds can be supported by such
objects, paralleling a result of Auroux, Donaldson and Katzarkov. Various
constructions of broken Lefschetz fibrations and a generalization of the symplectic
fiber sum operation to the near-symplectic setting are given. Extending the study of
Lefschetz fibrations, we detect certain constraints on the symplectic fiber sum
operation to result in a 4-manifold with nontrivial Seiberg–Witten invariant, as well
as the self-intersection numbers that sections of broken Lefschetz fibrations can
acquire.
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Keywords
four-manifold, Lefschetz fibration, round
handle, near-symplectic
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Mathematical Subject Classification
Primary: 57M50, 57R65
Secondary: 57R17
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Milestones
Received: 31 December 2007
Revised: 26 October 2008
Accepted: 4 December 2008
Published: 4 March 2009
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