Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proximal Vortex Cycles and Vortex Nerves. Non-Concentric, Nesting,
  Possibly Overlapping Homology Cell Complexes   This article introduces proximal planar vortex 1-cycles, resembling the
structure of vortex atoms introduced by William Thomson (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 (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.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin