We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse. The advantage of using strong collapses is the existence and uniqueness of cores and their relati...

A class of finite simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum* property depends only on the geometric realization and the field. Characterizations in terms of simplicial homology are given. It is proved that Buch...

The propagation of information in social, biological and technological systems represents a crucial component their dynamic behavior. When limited to pairwise interactions, rather firm grip is available on the relevant parameters critical transitions these spreading processes, most notably pandemic transition, which indicates conditions for spread cover large fraction network. challenge that, m...

Simplicial Complexes are used to model topology in Geographic Information Systems (GIS). Line intersection is an essential operation to update them. We introduce a finite-resolution line intersection method, called Zero Order Intersection, and apply it to simplicial complexes. Any reliable implementation of a line intersection algorithm has to address the limitations of a discrete computational...

We consider closed simplicial and cubical n-complexes in terms of link of their (n−2)faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every (n − 2)face is contained in 3 or 4 n-faces. Such simplicial complexes with short (i.e. of length 3 or 4) links are completely classified by their characteristic partition. We consider also embedding into hypercubes of the skele...