Deformations of circle-valued Morse functions on surfaces
Let M be a smooth connected orientable compact surface and let F_cov (M,S^1) be a space of all Morse functions f: M → S^1 without critical points on ∂M such that, for any connected component V of ∂M, the restriction f : V → S^1 is either a constant map or a covering map. The space F_cov (M,S^1) is endowed with the C^∞-topology. We present the classification of connected components of the space F_cov (M,S^1). This result generalizes the results obtained by Matveev, Sharko, and the author for the case of Morse functions locally constant on ∂M., number=10, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Maksimenko, S. I., year=2010, month=Oct., pages=1360–1366