Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reeb graph and quasi-states on the two-dimensional torus   This note deals with quasi-states on the two-dimensional torus. Quasi-states
are certain quasi-linear functionals (introduced by Aarnes) on the space of
continuous functions. Grubb constructed a quasi-state on the torus, which is
invariant under the group of area-preserving diffemorphisms, and which moreover
vanishes on functions having support in an open disk. Knudsen asserted the
uniqueness of such a quasi-state; for the sake of completeness, we provide a
proof. We calculate the value of Grubb's quasi-state on Morse functions with
distinct critical values via their Reeb graphs. The resulting formula coincides
with the one obtained by Py in his work on quasi-morphisms on the group of
area-preserving diffeomorphisms of the torus.

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc