Topological classification of circle-valued simple Morse-Bott functions on closed orientable surfaces

Deformations of circle-valued Morse functions on 2-torus

“…Morse-Bott functions are very popular object to research and were studied by many specialists in a variety of problems in topology and its applications. In particular topological classification of Morse-Bott functions on oriented surfaces were studied by E. B. Batista et al [2] and by J. Martínez-Alfaro et al [16]. I. Gelbukh classified Morse-Bott functions with the only 2 nondegenerate critical points on manifolds [4].…”

“…We can also describe functions listed above via so-called Kronrod-Reeb graphs, see for example [2,4]. A Kronrod-Reeb graph of a function from ( 1)-( 4) is a path graph, and a circle graph in the case (5).…”