Deformations in the General Position of the Optimal Functions on Oriented Surfaces with Boundary
We consider simple functions with nondegenerate singularities on smooth compact oriented surfaces with boundary. The relationship between the optimality and polarity of Morse functions, m-functions and mm-functions on smooth compact oriented connected surfaces is described. The concept of equipped Kronrod–Reeb graph is used to define deformation in the general position. Moreover, we present the entire list of deformations of simple functions of one of the classes described above on a torus, on a 2-dimensional disk with boundary, and on the connected sum of two tori.
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