CANONICAL FORM OF REEB GRAPH FOR MORSE FUNCTIONS ON SURFACES: INVERSION OF 2-SPHERE IN 3-SPACE
Elena Alexandrovna Kudryavtseva · International Journal of Shape Modeling · 1999
We discuss in the present paper the following natural question: is the space of all Morse functions with fixed number of minima and maxima on a closed surface linearly connected? We give an algorithm for reduction of any Morse function on a closed orientable surface to some canonical form. We apply this result to the new representation for the inversion of 2-sphere in Euclidean 3-space, in terms of Reeb graph of the height function.