Abstract:

A discrete Morse function for a simplicial complex describes how to construct a homotopy equivalent CW-complex with hopefully fewer cells. We associate a boolean function with the simplicial complex and construct a discrete Morse function using its Fourier transform.

Methods from theoretical computer science by O'Donnell, Saks, Schramm, and Servedio, together with experimental data on complexes from Hachimoro's library, provide some evidence that the constructed discrete Morse functions are efficient.