Low Dimensional Topology and Circle-Valued Morse Functions

Explore a 55-minute conference talk on low-dimensional topology and circle-valued Morse functions presented by Fabiola Manjarrez-Gutiérrez from Universidad Nacional Autónoma de México. Delve into the study of bounds on the handle number of sutured manifolds, examining geometric arguments that connect the Morse-Novikov number of a link to its tunnel number. Discover upper and lower bounds on the handle number of Heegaard splittings for sutured manifolds (M, λ) in relation to handle numbers of decompositions along surfaces representing 2nd homology classes. Investigate the development of the handle number function h: H_2(M, ∂M; ℝ) → ℕ, analyzing its properties such as boundedness, constancy on rays from the origin, and local maximality. Gain insights into this collaborative research conducted with Kenneth L. Baker, advancing understanding in the field of low-dimensional topology.