TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES - Batista, E. B.; Costa, J. C.F. [UNESP]; Meza-Sarmiento, I. S. (Journal of Singularities, 2022)
In this work we investigate the topological classification of circle-valued simple Morse-Bott functions on connected closed orientable surfaces, up to topological conjugacy. We provide a complete topological invariant, called the MB-Reeb graph. This invariant is based on the generalized Reeb graph and the topological type of singular level sets of these functions. The results presented here extend to those obtained by the authors in a previous work when the surface is the standard sphere.
Keywords: Morse–Bott functions; Reeb graph; topological equivalence; Topological invariant