Gauge Theory and Topology Seminar: Open book decompositions and Morse complexity

An open book decomposition of a manifold is a structure generalizing a fibration over the circle. In odd dimensions, every closed oriented manifold admits an open book decomposition; in even dimensions, the picture is murkier. We show that many locally symmetric manifolds do not admit open book decompositions and explain a connection to Morse complexity, a semi-norm on homology introduced by Gromov, for which we give new computations. This is joint work with Fedor Manin and Shmuel Weinberger.