Low Dimensional Topology and Circle-Valued Morse Functions

This course covers bounds on the handle number of sutured manifolds based on geometric arguments for bounding the Morse-Novikov number of a link. Students will learn to obtain upper and lower bounds on the handle number of a Heegaard splitting of a sutured manifold in terms of its decompositions along a surface representing a given 2nd homology class. The course introduces the handle number function, which is bounded, constant on rays from the origin, and locally maximal. The teaching method involves presenting joint work with Kenneth L. Baker. This course is intended for individuals interested in low-dimensional topology and circle-valued Morse functions.