Inanc Baykur:
Topological complexity of symplectic 4-manifolds and Stein fillings
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Abstract: Following the ground-breaking works of Donaldson and Giroux,
Lefschetz pencils and open books have become central tools in the
study of symplectic 4-manifolds and contact 3-manifolds. An open
question at the heart of this relationship is whether or not there
exists an a priori bound on the topological complexity of a symplectic
4-manifold, coming from the genus of a compatible Lefschetz pencil on
it, and a similar question inquires if there is such a bound on any
Stein filling of a fixed contact 3-manifold, coming from the genus of
a compatible open book. We will present our solutions to both
questions, making heroic use of positive factorizations in surface
mapping class groups of various flavors. This is joint work with J.
Van Horn-Morris.