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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 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].

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/