Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy BV-algebra structure on the double cobar construction   We show that the double cobar construction, $\Omega^2 C_*(X)$, of a
simplicial set $X$ is a homotopy BV-algebra if $X$ is a double suspension, or
if $X$ is 2-reduced and the coefficient ring contains the ring of rational
numbers $\mathbb{Q}$. Indeed, the Connes-Moscovici operator defines the desired
homotopy BV-algebra structure on $\Omega^2 C_*(X)$ when the antipode $S :
\Omega C_*(X) \to \Omega C_*(X)$ is involutive. We proceed by defining a family
of obstructions $O_n : \widetilde{C}_*(X) \to \widetilde{C}_*(X)^{\otimes n}$,
$n\geq 2$ measuring the difference $S^2 - Id$. When $X$ is a suspension, the
only obstruction remaining is $O_2 := E^{1,1} - \tau E^{1,1}$ where $E^{1,1}$
is the dual of the $\smile_1$-product. When $X$ is a double suspension the
obstructions vanish.

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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: cs
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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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: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: econ