Special equipped Morse functions on surfaces / E. A. Kudryavtseva. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 4. P. 14-20 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

Let M be a smooth closed orientable surface. Let F be the space of Morse functions on M, and F¹ be the space of framed Morse functions, both endowed with the C^∞-topology. The space F⁰ of special framed Morse functions is defined. We prove that the inclusion mapping F⁰→F¹ is a homotopy equivalence. In the case when at least χ(M)+1 critical points of each function of F are labeled, the homotopy equivalences K∼M and F∼F⁰∼D⁰×K are proved, where K is the complex of framed Morse functions, M≈F¹/D⁰ is the universal moduli space of framed Morse functions, D⁰ is the group of self-diffeomorphisms of M homotopic to the identity.

Key words: Morse function, framed Morse function, complex of framed Morse functions, C^∞-topology, universal moduli space.