Blob homology

Morrison, Scott¹ ; Walker, Kevin²

¹ Department of Mathematics, University of California, Berkeley, Berkeley CA 94720, USA
² Microsoft Station Q, University of California, Santa Barbara CA 93106-6105, USA

Geometry & topology, Tome 16 (2012) no. 3, pp. 1481-1607.

Résumé

Given an $n$–manifold $M$ and an $n$–category $\mathcal{C}$, we define a chain complex (the “blob complex”) ${\mathcal{ℬ}}_{\ast }\left(M;\mathcal{C}\right)$. 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].

Détail

DOI : 10.2140/gt.2012.16.1481

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

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