# Jeremy Van Horn-Morris : Fiber genus and the topology of symplectic fillings

Work of Donaldson, Giroux, and many others shows how to associate a singular surface fibration to a symplectic 4-manifold, either closed or with boundary, as well as to a contact 3-manifold. These are Lefschetz pencils, fibrations and open books, resp. It was asked by Stipsicz, Ozbagci, Korkmaz and others, whether the genus (or genus and self intersection) of the fiber of these fibrations gave an a priori bound on the topological complexity of the symplectic manifold. This question is equivalent to asking for a bound on the length of a factorization of a mapping class element of the fiber into right handed Dehn twists. We will discuss some of the known conditions which can produce such a bound, as well as present examples where such a bound does not exist. This is joint work with I. Baykur.

**Category**: Geometry and Topology**Duration**: 01:34:52**Date**: April 16, 2013 at 4:25 PM**Views**: 127-
**Tags:**seminar, Geometry/topology Seminar

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