Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operations on Metric Thickenings   Many simplicial complexes arising in practice have an associated metric space
structure on the vertex set but not on the complex, e.g. the Vietoris-Rips
complex in applied topology. We formalize a remedy by introducing a category of
simplicial metric thickenings whose objects have a natural realization as
metric spaces. The properties of this category allow us to prove that, for a
large class of thickenings including Vietoris-Rips and Cech thickenings, the
product of metric thickenings is homotopy equivalent to the metric thickenings
of product spaces, and similarly for wedge sums.

32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat