Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces

Michał Lipiński, Jacek Kubica, Marian Mrozek, Thomas Wanner

Published 2019-11-28Version 1

In this paper we present the theory of combinatorial multivector fields in finite topological spaces. It generalizes the analogous theory for Lefschetz complexes recently introduced in \cite{Mr2017}. We drop the restrictive assumpion in \cite{Mr2017} that every multivector has a unique maximal element. In this setting we define isolated invariant sets, isolating neighborhood and index pairs and we construct the Conley index. We prove its additivity property.