Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integration of singular foliations via paths   We give a new construction of the holonomy and fundamental groupoids of a
singular foliation. In contrast with the existing construction of Androulidakis
and Skandalis, our method proceeds by taking a quotient of an infinite
dimensional space of paths. This strategy is a direct extension of the
classical construction for regular foliations and mirrors the integration of
Lie algebroids via paths (per Crainic and Fernandes). In this way, we obtain a
characterization of the holonomy and fundamental groupoids of a singular
foliation that more clearly reflects the homotopic character of these
invariants. As an application of our work, we prove that the constructions of
the fundamental and holonomy groupoid of a foliation have functorial
properties.

31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph