Morse-Novikov Numbers of 3-Manifolds

Explore a 42-minute lecture by Ken Baker from the University of Miami discussing Morse-Novikov numbers of 3-manifolds. Learn how the Morse-Novikov number counts the minimum number of critical points among Morse representatives within a homotopy class of circle valued functions on a 3-manifold. Discover how circle valued Morse functions can be recast as 'handle numbers' when viewed through their associated handle decompositions, and how the theories of generalized Heegaard splittings and sutured manifolds advance our understanding of these mathematical concepts. The lecture surveys key results and curious phenomena developed through Baker's research, including joint works with Fabiola Manjarrez-Gutierrez, providing valuable insights into this specialized area of mathematics.