The lattice path operad and Hochschild cochains

We introduce two coloured operads in sets -- the lattice path operad and a cyclic extension of it -- closely related to iterated loop spaces and to universal operations on cochains. As main application we present a formal construction of an $E_2$-action (resp. framed $E_2$-action) on the Hochschild cochain complex of an associative (resp. symmetric Frobenius) algebra.

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