Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Morse theory of \v{C}ech and Delaunay complexes   Given a finite set of points in $\mathbb R^n$ and a radius parameter, we
study the \v{C}ech, Delaunay-\v{C}ech, Delaunay (or Alpha), and Wrap complexes
in the light of generalized discrete Morse theory. Establishing the \v{C}ech
and Delaunay complexes as sublevel sets of generalized discrete Morse
functions, we prove that the four complexes are simple-homotopy equivalent by a
sequence of simplicial collapses, which are explicitly described by a single
discrete gradient field.

24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex