Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A glimpse into the differential topology and geometry of optimal
  transport   This note exposes the differential topology and geometry underlying some of
the basic phenomena of optimal transportation. It surveys basic questions
concerning Monge maps and Kantorovich measures: existence and regularity of the
former, uniqueness of the latter, and estimates for the dimension of its
support, as well as the associated linear programming duality. It shows the
answers to these questions concern the differential geometry and topology of
the chosen transportation cost. It also establishes new connections --- some
heuristic and others rigorous --- based on the properties of the
cross-difference of this cost, and its Taylor expansion at the diagonal.

35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg