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Special framed Morse functions on surfaces

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    E. A. Kudryavtseva

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  1. E. A. Kudryavtseva
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Original Russian Text © E.A. Kudryavtseva, 2012, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2012, Vol. 67, No. 4, pp. 14–20.

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Kudryavtseva, E.A. Special framed Morse functions on surfaces. Moscow Univ. Math. Bull. 67, 151–157 (2012). https://doi.org/10.3103/S0027132212040031

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