Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contractions in persistence and metric graphs   We prove that the existence of a $1$-Lipschitz retraction (a contraction)
from a space $X$ onto its subspace $A$ implies the persistence diagram of $A$
embeds into the persistence diagram of $X$. As a tool we introduce tight
injections of persistence modules as maps inducing the said embeddings. We show
contractions always exist onto shortest loops in metric graphs and conjecture
on existence of contractions in planar metric graphs onto all loops of a
shortest homology basis.
  Of primary interest are contractions onto loops in geodesic spaces. These act
as ideal circular coordinates. Furthermore, as the Theorem of Adamaszek and
Adams describes the pattern of persistence diagram of $S^1$, a contraction $X
\to S^1$ implies the same pattern appears in persistence diagram of $X$.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph