Abstract
Let be a smooth closed orientable surface. Let be the space of Morse functions on with a fixed number of critical points of each index such that at least critical points are labelled by different labels (numbered). The notion of a skew cylindric-polyhedral complex is introduced, which generalizes the notion of a polyhedral complex. The skew cylindric-polyhedral complex (“the complex of framed Morse functions”) associated with the space is defined. In the case the polytope is finite; its Euler characteristic is calculated and the Morse inequalities for its Betti numbers are obtained. The relation between the homotopy types of the polytope and the space of Morse functions equipped with the -topology is indicated.Bibliography: 51 titles.
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