28 citations · 28 across the 2 of their papers we have counts for
3 papers
math.DS2019★ 28 cited
Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
Michał Lipiński, Jacek Kubica, Marian Mrozek +1
We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in \cite{Mr2017}. The generalization consists in dropping the restrictive as…
math.AT2019
Lefschetz Complexes as Finite Topological Spaces
Jacek Kubica, Marian Mrozek
We consider a fixed basis of a finitely generated free chain complex as a finite topological space and we present a sufficient condition for the singular homology of this space to…
math.AT2018
Persistent Homology of Morse Decompositions in Combinatorial Dynamics
Tamal K. Dey, Mateusz Juda, Tomasz Kapela +3
We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and…