We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions. This settles a question raised by Chari and Joswig. In the 1-dimensional case, this implies that the complex ...

We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related ...

The main objective of this thesis is to analyze a generalization of Morse's theory in the case of stratified spaces. The content is divided into three main parts. In the first part we present the background of the classical ...

We develop a new method to compute the homology groups of Alexandroff topological spaces (or equivalently of partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding ...