Abstract

Applications of computational topology  in computational science and engineering are many and growing. Morse theory is a fundamental tool for investigating different complexes. Discrete Morse theory is a tool dealing with problems of discrete mathematical structures. Discrete Morse theory in turn built on Whitehead’s simple homotopy theory, in 1939 and developed by Forman from the classical smooth Morse theory in 1988. A discrete mathematical structure we usually consider consisting of points, lines, triangles, tetrahedrons, and their higher-dimensional analogs. By observation, simplicial complexes are built by points, lines, triangles, tetrahedrons, and their higher-dimensional analogs. Therefore, simplifying problems of simplicial complexes can be solved by discrete Morse theory.