Abstract
In this paper, as a new contribution to the tensor-centric warfare (TCW) series [1] [2] [3] [4], we extend the kinetic TCW-framework to include non-kinetic effects, by addressing a general systems confrontation [5], which is waged not only in the traditional physical Air-Land-Sea domains, but also simultaneously across multiple non-physical domains, including cyberspace and social networks. Upon this basis, this paper attempts to address a more general analytical scenario using rigorous topological methods to introduce a two-level topological representation of modern armed conflict; in doing so, it extends from the traditional red-blue model of conflict to a red-blue-green model, where green represents various neutral elements as active factions; indeed, green can effectively decide the outcomes from red-blue conflict. System confrontations at various stages of the scenario will be defined by the non-equilibrium phase transitions which are superficially characterized by sudden entropy growth. These will be shown to have the underlying topology changes of the systems-battlespace. The two-level topological analysis of the systems-battlespace is utilized to address the question of topology changes in the combined battlespace. Once an intuitive analysis of the combined battlespace topology is performed, a rigorous topological analysis follows using (co)homological invariants of the combined systems-battlespace manifold.
Highlights
To start with the systems-battlespace topology, we introduce an important concept from differential topology: 5Recall that in our initial kinetic scenario we have n = 30 aircraft on each side
In this subsection, the symbol λ is reserved for the eigenvalues of the Laplacian ∆t, while p is reserved for the rank of thehomology groups
Neutral parties caught in the situation, to aims of causing system failure that undercuts an opposition’s ability or willingness to fight, simultaneous conflict occurring across multiple domains without definable lines, and foundational international and national legal and social expectations about human, environmental and social consequences of armed conflict
Summary
Research Investment (SRI) is to better enable dealing with uncertainty, meaning achieving reliable decision-making in environments that are non-ergodic. To utilize the geometric framework most suitable for the present topological analysis, we will assume that Red and Blue (as well as Green) configuration manifolds, M Red , M Blue and M Green , are endowed with the pseudo-Riemannian geometry, which is both elliptic (positive metric) and hyperbolic [7] [8]), defined by their corresponding ( ) quadratic forms, Aab Ra Rb , Cab Ba Bb and ( ) γ Aab + Cab Ra Rb + Ba Bb. To utilize the geometric framework most suitable for the present topological analysis, we will assume that Red and Blue (as well as Green) configuration manifolds, M Red , M Blue and M Green , are endowed with the pseudo-Riemannian geometry, which is both elliptic (positive metric) and hyperbolic
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