Claremont Topology Seminar: Sierra Knavel (Georgia Tech)

We especially welcome all undergraduates and graduate students to attend topology seminar!

Speaker: Sierra Knavel (Georgia Tech)

Title: Betti Numbers and Indecomposability of Genus-2 Lefschetz Fibrations

Abstract: Symplectic 4-manifolds, smooth 4-manifolds equipped with a closed, nondegenerate 2-form, arise naturally in classical mechanics and have become central objects of study in topology. Following foundational work by Donaldson and Gompf, Lefschetz pencils have been shown to correspond bijectively with symplectic 4-manifolds, making symplectic 4-manifolds a tractable family of smooth 4-manifolds to work with. This talk focuses on genus-2 Lefschetz fibrations obtained by blowing up Lefschetz pencils and presents new bounds on their first Betti number. We will also examine a particularly elusive class of non-simply connected, indecomposable genus-2 fibrations and consider the prospects of extending these results to higher genera.