Deformation Theories Controlled by Hochschild Cohomologies
Abstract
We explore how the higher order Hochschild cohomology controls a deformation theory when the simplicial set models the 3-sphere. Besides generalizing to the d-sphere for any d≥1, we also investigate a deformation theory corresponding to the tertiary Hochschild cohomology, which naturally reduces to those studied for the secondary and usual Hochschild cohomologies under certain conditions.
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