Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Death and extended persistence in computational algebraic topology   The main aim of this paper is to explore the ideas of persistent homology and
extended persistent homology, and their stability theorems, using ideas from
[Bubenik and Scott, 2014; Cohen-Steiner, Edelsbrunner, and Harer, 2007; and
Cohen-Steiner, Edelsbrunner, and Harer, 2009], as well as other sources. The
secondary aim is to explore the homology (and cohomology) of non-orientable
surfaces, using the Klein bottle as an example. We also use the Klein bottle as
an example for the computation of (extended) persistent homology, referring to
it throughout the paper.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc