The blob complex

Details The blob complex The blob complex

2010-09-25

arxiv.org/abs/1009.5025v3

Mathematics

Algebraic Topology

106 pages. Version 3 contains many improvements following suggestions from the referee and others, and some additional materia

Scientific paper

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 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 definition of a weak n-category with strong duality which is particularly well suited for work with TQFTs.

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