The blob complex

By S. Morrison, Kevin Walker. 2010

47 citations recorded by the source corpus.

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 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/048c8e8e5231614f42b04d0d252a0b67a88f7f90

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Higher Hochschild Homology, Topological Chiral Homology and Factorization Algebras (2010, methodology): “of Morrison-Walker is equivalent to an unoriented variant of topological chiral homology. We brieﬂy explain here how to deduce this equivalence from the proof of Theorem 5 and several statements from [29]. The main diﬀerence with §5.1 and §5.2 to keep in mind is that we no longer assume our manifold”
Functoriality of colored link homologies (2017, background): “Functoriality in S(3) is also the only missing ingredient for upgrading Khovanov–Rozansky link homologies to invariants of 4-manifolds with links in their boundary: it should allow the Khovanov–Rozansky invariants to be assembled into a disk-like 4-category as in [39], which then gives rise to a (4 ”
The finiteness conjecture for skein modules (2019, methodology): “We expect that the techniques of blob homology [74] and the β version of factorization homology [3] might be useful to”
Supersymmetric gauge theory and the Yangian (2013, methodology): “dal category Fin(Y(g)) can be viewed as a 2-category with one object, whose 1-morphisms are objects of Fin(Y(g)). Let us call this 2-category Fin(2)(Y(g)). Ayala-Rozenblyum [AR13] and Morrison-Walker [MW10] have developed a theory of higher Hochschild homology for 2-categories. I will use the theory”