Special framed Morse functions on surfaces
Elena Alexandrovna Kudryavtseva · Moscow University Mathematics Bulletin · 2012
Let M be a smooth closed orientable surface. Let F be the space of Morse functions on M and $$\mathbb{F}^1$$ be the space of framed Morse functions both endowed with the C ∞-topology. The space $$\mathbb{F}^0$$ of special framed Morse functions is defined. We prove that the inclusion mapping is a homotopy equivalence. In the case when at least x(M) + 1 critical points of each function of F are marked, the homotopy equivalences and are proved, where is the complex of framed Morse functions, is the universal moduli space of framed Morse functions, is the group of self-diffeomorphisms of M homotopic to the identity.