by the NSF grant DMS 0856196, Regent’s Faculty Fellowship, and the Grant for Support of Scientific Schools NSh-3036.2008.2.

Preliminaries {#sect:prelim}
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Notation and conventions
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The ground field ${{\mathbb K}}$ has the zero characteristic. Depending on a context our underlying symmetric monoidal category is either the category of graded vector spaces, or the category of cochain complexes, or the category of compactly generated topological spaces. By suspension ${{\bf s}}V$ of a graded vector space (or a chain complex) $V$ we mean ${{\varepsilon}}\otimes V$, where ${{\varepsilon}}$ is a one-dimensional vector space placed in degree $+1$. For a vector $v\in V$ we denote by $|v|$ its degree. $S_n$ denotes the symmetric group on $n$ letters and ${{\rm Sh}}_{p,q}$ denotes the subset of $(p,q)$-shuffles in $S_{p+q}$.

For a graded vector space (or a cochain complex) $V$ the notation $S(V)$ (resp. ${{\underline{S}}}(V)$) is reserved for the symmetric algebra (resp. truncated symmetric algebra) of $V$: $$S(V) = {{\mathbb K}}\oplus V \oplus S^2(V) \oplus S^3(V) \oplus \dots\,,$$ $${{\underline{S}}}(V) =  V \oplus S^2(V) \oplus S^3(V) \oplus \dots\,.$$ Similarly, $T(V)$ (resp. ${{\underline{T}}}(V)$) denotes the tensor algebra (resp. truncated tensor algebra) of $V$: $$T(V) = {{\mathbb K}}\oplus V \oplus V^{\otimes  2}  \oplus  V^{\otimes  3} \oplus \dots\,,$$ $${{\underline{T}}}(V) =  V 