Blob homology

Morrison, Scott; Walker, Kevin

doi:10.2140/gt.2012.16.1481

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Blob homology

Scott Morrison and Kevin Walker

Geometry & Topology 16 (2012) 1481–1607

DOI: 10.2140/gt.2012.16.1481

Abstract

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 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

Mathematical Subject Classification 2010

Primary: 57R56

References

Publication

Received: 19 October 2010

Revised: 19 December 2011

Accepted: 25 April 2012

Published: 25 July 2012

Proposed: Peter Teichner

Seconded: Ralph Cohen, Mike Freedman

Authors

Scott Morrison
Department of Mathematics University of California, Berkeley Berkeley CA 94720 USA
http://tqft.net/
Kevin Walker
Microsoft Station Q University of California Santa Barbara CA 93106-6105 USA
http://canyon23.net/math/

Volume 16, issue 3 (2012)