Abstract
A spatial refinement of Bar-Natan homology is given, that is, for any link diagram [Formula: see text] we construct a CW-spectrum [Formula: see text] whose reduced cellular cochain complex gives the Bar-Natan complex of [Formula: see text]. The stable homotopy type of [Formula: see text] is a link invariant and is described as the wedge sum of the “canonical sphere spectra”. We conjecture that the quantum filtration of Bar-Natan homology also lifts to the spatial level, and that it leads us to a cohomotopical refinement of the [Formula: see text]-invariant.
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