Higher categories, colimits, and the blob complex

Abstract

We summarize our axioms for higher categories, and describe the blob complex. Fixing an n-category C, the blob complex associates a chain complex B_*(W;C)$ to any n-manifold W. The 0-th homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when W=S^1 they coincide). The blob complex has a very natural definition in terms of homotopy colimits along decompositions of the manifold W. We outline the important properties of the blob complex, and sketch the proof of a generalization of Deligne's conjecture on Hochschild cohomology and the little discs operad to higher dimensions.

7 pages

References in corpus (5)

• On the Classification of Topological Field Theories
• On piecewise linear cell decompositions
• A categorification of the stable SU(2) Witten-Reshetikhin-Turaev invariant of links in S2 x S1
• Derived Algebraic Geometry VI: E_k Algebras
• Higher categories, colimits, and the blob complex

Cited by in corpus (7)

• Short-range entanglement and invertible field theories
• On dualizability of braided tensor categories
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• Excision of Skein Categories and Factorisation Homology
• Condensations in higher categories
• Higher categories, colimits, and the blob complex
• Deformation Quantization via Categorical Factorization Homology