Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Excision Theorem for Persistent Homology   We demonstrate that an excision property holds for persistent homology
groups. This property holds for a large class of filtrations, and in fact we
show that given any filtration on a larger space, we can extend it to a
filtration of two subspaces which guarantees that the excision property holds
for the triple. This method also applies to the Mayer-Vietoris sequence in
persistent homology introduced by DiFabio and Landi in 2011, extending their
results to a much larger class of filtrations.

35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc