#### Volume 16, issue 3 (2012)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Blob homology

### Scott Morrison and Kevin Walker

Geometry & Topology 16 (2012) 1481–1607
##### Abstract

Given an $n$–manifold $M$ and an $n$–category $\mathsc{C}$, we define a chain complex (the “blob complex”) ${\mathsc{ℬ}}_{\ast }\left(M;\mathsc{C}\right)$. 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 definition of a weak $n$–category with strong duality which is particularly well suited for work with TQFTs. This is the published version of [arXiv 1009.5025].

##### Keywords
topological quantum field theory, Hochschild homology, Deligne conjecture
Primary: 57R56