Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On polytopal upper bound spheres   Generalizing a result (the case $k = 1$) due to M. A. Perles, we show that
any polytopal upper bound sphere of odd dimension $2k + 1$ belongs to the
generalized Walkup class ${\cal K}_k(2k + 1)$, i.e., all its vertex links are
$k$-stacked spheres. This is surprising since the $k$-stacked spheres minimize
the face-vector (among all polytopal spheres with given $f_0,..., f_{k - 1}$)
while the upper bound spheres maximize the face vector (among spheres with a
given $f_0$).
  It has been conjectured that for $d\neq 2k + 1$, all $(k + 1)$-neighborly
members of the class ${\cal K}_k(d)$ are tight. The result of this paper shows
that, for every $k$, the case $d = 2k +1$ is a true exception to this
conjecture.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg