This monograph covers in a unified manner new results on smooth functions on manifolds. A major topic is Morse and Bott functions with a minimal number of singularities on manifolds of dimension greater than five. Sharko computes obstructions to deformation of one Morse function into another on a simply connected manifold. In addition, a method is developed for constructing minimal chain complexes and homotopical systems in the sense of Whitehead. This leads to conditions under which Morse functions on non-simply-connected manifolds exist. Sharko also describes new homotopical invariants of manifolds, which are used to substantially improve the Morse inequalities. The conditions guaranteeing the existence of minimal round Morse functions are discussed.
Frechet manifolds Minimal Morse functions on simply connected manifolds Stable algegra Homotopy of chain complexes Morse numbers and minimal Morse functions Elements of the homotopy theory of non-simply-connected CW-complexes Minimal Morse functions of non-simply-connected manifolds Minimal round Morse functions Bibliography.