Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex numbers of simplicial complexes with free abelian fundamental
  group   We show that the minimum number of vertices of a simplicial complex with
fundamental group $\mathbb{Z}^{n}$ is at most $O(n)$ and at least
$\Omega(n^{3/4})$. For the upper bound, we use a result on orthogonal
1-factorizations of $K_{2n}$. For the lower bound, we use a fractional
Sylvester-Gallai result. We also prove that any group presentation $\langle S |
R\rangle \cong \mathbb{Z}^{n}$ whose relations are of the form
$g^{a}h^{b}i^{c}$ for $g, h, i \in S$ has at least $\Omega(n^{3/2})$
generators.

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The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs