Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spaces of nonpositive curvature arising from a finite algebra   In this paper we introduce a family of examples that can be regarded as
spaces of nonpositive curvature, but with the distinct quality that they are
not complete as metric spaces. This amounts to the fact that they are modelled
on a finite von Neumann algebra, and the metrics introduced arise from the
trace of the algebra. In spite of the noncompleteness of these manifolds, their
geometry can be studied from the view-point of metric geometry, and several
techniques derived from the functional analysis are applied to gain insight on
their geodesic structure.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph