Geometry & Topology

Blob homology

Scott Morrison and Kevin Walker

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Given an n–manifold M and an n–category C, we define a chain complex (the “blob complex”) (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 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].

Article information

Geom. Topol., Volume 16, Number 3 (2012), 1481-1607.

Received: 19 October 2010
Revised: 19 December 2011
Accepted: 25 April 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R56: Topological quantum field theories

topological quantum field theory Hochschild homology Deligne conjecture


Morrison, Scott; Walker, Kevin. Blob homology. Geom. Topol. 16 (2012), no. 3, 1481--1607. doi:10.2140/gt.2012.16.1481.

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