2022/02/21 by Tomoo Yokoyama, Yokoyama, Tomoo
Mathematics · #Algebra over a field #Base (topology) #Computer science #Decomposition #Dynamical Systems (math.DS) #FOS: Mathematics #Filtration (mathematics) #General Topology (math.GN) #Generalization #Geometric and Algebraic Topology #Group (periodic table) #Group action #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Pure mathematics #Set (abstract data type)
paper · pdf · doi:10.48550/arxiv.2202.10568
openalex publication_date 2022/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper constructs a foundation to analyze semi-group actions, group actions, filtrations, and decompositions in a unified manner. In fact, though the studies of decomposition can be applied to foliated spaces and group actions, they can not be applied to semi-group actions and filtrations in general because filtration and the set of orbits of a semi-group need not be decompositions of the base spaces. To analyze these concepts in a unified manner, we introduce a concept of a semi-decomposition which is a natural generalization of these concepts because similar relations among recurrence and their variants to group actions and decompositions hold for semi-decompositions. On the other hand, we demonstrate the difference between the recurrent concepts for group actions and those even for semi-group actions.