Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Centrally symmetric manifolds with few vertices   A centrally symmetric $2d$-vertex combinatorial triangulation of the product
of spheres $\S^i\times\S^{d-2-i}$ is constructed for all pairs of non-negative
integers $i$ and $d$ with $0\leq i \leq d-2$. For the case of $i=d-2-i$, the
existence of such a triangulation was conjectured by Sparla. The constructed
complex admits a vertex-transitive action by a group of order $4d$. The crux of
this construction is a definition of a certain full-dimensional subcomplex,
$\B(i,d)$, of the boundary complex of the $d$-dimensional cross-polytope. This
complex $\B(i,d)$ is a combinatorial manifold with boundary and its boundary
provides a required triangulation of $\S^i\times\S^{d-i-2}$. Enumerative
characteristics of $\B(i,d)$ and its boundary, and connections to another
conjecture of Sparla are also discussed.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat