Connected components of the space of circle-valued Morse functions on surfaces
Sergiy Maksymenko · arXiv (Cornell University) · 1999
We classify the path-components of the space of circle-valued Morse functions on compact surfaces: two Morse functions $f, g: M\to S^1$ belong to same path-component of this space if and only if they are homotopic and have equal numbers of critical points at each index.