Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polytopal Bier spheres and Kantorovich-Rubinstein polytopes of weighted
  cycles   The problem of deciding if a given triangulation of a sphere can be realized
as the boundary sphere of a simplicial, convex polytope is known as the
"Simplicial Steinitz problem". It is known by an indirect and non-constructive
argument that a vast majority of Bier spheres are non-polytopal. Contrary to
that, we demonstrate that the Bier spheres associated to threshold simplicial
complexes are all polytopal. Moreover, we show that all Bier spheres are
starshaped. We also establish a connection between Bier spheres and
Kantorovich-Rubinstein polytopes by showing that the boundary sphere of the
KR-polytope associated to a polygonal linkage (weighted cycle) is isomorphic to
the Bier sphere of the associated simplicial complex of "short sets".

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc