Given an n-manifold M and an n-category C, we define a chain complex (the "blob complex") B*(M;C). The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, and also as a generalization of Hochschild homology to n-categories and n-manifolds. It enjoys a number of nice formal properties, including a higher dimensional generalization of Deligne's conjecture about the action of the little disks operad on Hochschild cochains. Along the way, we give a...[Show more]
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|Source:||Geometry and Topology|
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