Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euler characteristic numbers of space-like manifolds   In this note, we prove that if a compact even dimensional manifold $M^{n}$
with negative sectional curvature is homotopic to some compact space-like
manifold $N^{n}$, then the Euler characteristic number of $M^{n}$ satisfies
$(-1)^{\frac{n}{2}}\chi(M^{n})>0$. We also show that the minimal volume
conjecture of Gromov is true for all compact even dimensional space-like
manifolds.

10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat