Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes

Authors : James F. PETERS

Pages : 56-72

Doi:10.33187/jmsm.425066

View : 10 | Download : 5

Publication Date : 2018-09-30

Article Type : Research Paper

Abstract :This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson insert ignore into journalissuearticles values(Lord Kelvin); in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson`s model of a vortex atom, inspired by P.G. Tait`s smoke rings. A vortex cycle is a collection of non-concentric, nesting 1-cycles with nonempty interiors i.e., a collection of 1-cycles that share a nonempty set of interior points and which may or may not overlap);. Overlapping 1-cycles in a vortex yield an Edelsbrunner-Harer nerve within the vortex. Overlapping vortex cycles constitute a vortex nerve complex. Several main results are given in this paper, namely, a Whitehead CW topology and a Leader uniform topology are outcomes of having a collection of vortex cycles insert ignore into journalissuearticles values(or nerves); equipped with a connectedness proximity and the case where each cluster of closed, convex vortex cycles and the union of the vortex cycles in the cluster have the same homotopy type.
Keywords : Connectedness Proximity, CW Topology, Vortex Cycle, Vortex Nerve, Vortex Nerve