Topological classification of simple Morse Bott functions on surfaces
J. Martínez-Alfaro, I. Meza-Sarmiento, R. Oliveira · Contemporary mathematics - American Mathematical Society · 2016
We present a global topological classification of Morse Bott functions on orientable closed surfaces. The invariant is based on the Reeb graph of the function and the topological type of the singular level sets. Connection with other known invariants it is shown. We also prove a realization Theorem of the Morse Bott functions.