Morse functions on simple polyhedra and a related way of presenting special spines of manifolds (Q1876459)

The author introduces a notion of Morse type function on spines of three-dimensional manifolds. A criterion for a spine to be special is given in terms of the number of critical points of a Morse type function. A connection is revealed between the complexity of a manifold and the types of critical points of some fixed Morse function on its minimal spine. This is an English translation of the author's article published in the book [\textit{Yu. G. Reshetnyak} (ed.) et al., Proceedings of the conference `Geometry and applications' dedicated to the 70th anniversary of Prof. Victor Toponogov. Novosibirsk: Izdatel'stvo Instituta Matematiki (2001; Zbl 1004.57017)].