Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Data and homotopy types   This paper presents explicit assumptions for the existence of interleaving
homotopy equivalences of both Vietoris-Rips and Lesnick complexes associated to
an inclusion of data sets. Consequences of these assumptions are investigated
on the space level, and for corresponding hierarchies of clusters and their
sub-posets of branch points. Hierarchy posets and branch point posets admit a
calculus of least upper bounds, which is used to show that the map of branch
points associated to the inclusion of data sets is a controlled homotopy
equivalence.

34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph