Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A 15-vertex triangulation of the quaternionic projective plane   In 1992, Brehm and K\"uhnel constructed a 8-dimensional simplicial complex
$M^8_{15}$ with 15 vertices as a candidate to be a minimal triangulation of the
quaternionic projective plane. They managed to prove that it is a manifold
"like a projective plane" in the sense of Eells and Kuiper. However, it was not
known until now if this complex is PL homeomorphic (or at least homeomorphic)
to $\mathbb{H}P^2$. This problem was reduced to the computation of the first
rational Pontryagin class of this combinatorial manifold. Realizing an
algorithm due to Gaifullin, we compute the first Pontryagin class of
$M^8_{15}$. As a result, we obtain that it is indeed a minimal triangulation of
$\mathbb{H}P^2$.

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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: alg-geom