The blob complex
Algebraic Topology
2014-11-11 v3 Category Theory
Geometric Topology
Quantum Algebra
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 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.
Keywords
Cite
@article{arxiv.1009.5025,
title = {The blob complex},
author = {Scott Morrison and Kevin Walker},
journal= {arXiv preprint arXiv:1009.5025},
year = {2014}
}
Comments
106 pages. Version 3 contains many improvements following suggestions from the referee and others, and some additional material