Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nondegenerate $2 \times k \times (k+1)$ Hypermatrices   We construct an extension of Gaussian elimination to show that if
$\mathbb{F}$ is a topological field, then there is a transitive, free, and
continuous action of a natural quotient of $GL_k(\mathbb{F}) \times
GL_{k+1}(\mathbb{F})$ on the set $M_k(\mathbb{F})$ of $2 \times k \times (k+1)$
hypermatrices over $\mathbb{F}$ with nonzero hyperdeterminant.
  We use this action to answer a number of questions including determining the
homotopy groups of $M_k(\mathbb{C})$, counting elements of $M_k(\mathbb{F}_q)$
(generalizing an unpublished result of Lewis and Sam), and computing
hyperdeterminants for $2 \times k \times (k+1)$ hypermatrices in $O(k^4)$ time,
which we use to compute explicit formulas in some special cases.

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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ