Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Whitehead products in moment-angle complexes and substitution of
  simplicial complexes   We study the question of realisability of iterated higher Whitehead products
with a given form of nested brackets by simplicial complexes, using the notion
of the moment-angle complex $Z_K$. Namely, we say that a simplicial complex $K$
realises an iterated higher Whitehead product $w$ if $w$ is a nontrivial
element of $\pi_*(Z_K)$. The combinatorial approach to the question of
realisability uses the operation of substitution of simplicial complexes: for
any iterated higher Whitehead product $w$ we describe a simplicial complex
$\partial\Delta_w$ that realises $w$. Furthermore, for a particular form of
brackets inside $w$, we prove that $\partial\Delta_w$ is the smallest complex
that realises $w$. We also give a combinatorial criterion for the nontriviality
of the product $w$. In the proof of nontriviality we use the Hurewicz image of
$w$ in the cellular chains of $Z_K$ and the description of the cohomology
product of $Z_K$. The second approach is algebraic: we use the coalgebraic
versions of the Koszul and Taylor complex for the face coalgebra of $K$ to
describe the canonical cycles corresponding to iterated higher Whitehead
products $w$. This gives another criterion for realisability of $w$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex