topological chiral homology in nLab
Context
Cohomology
Special and general types
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group cohomology, nonabelian group cohomology, Lie group cohomology
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cohomology with constant coefficients / with a local system of coefficients
Special notions
Variants
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differential cohomology
Operations
Theorems
Higher algebra
Algebraic theories
Algebras and modules
Higher algebras
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symmetric monoidal (∞,1)-category of spectra
Model category presentations
Geometry on formal duals of algebras
Theorems
Contents
Idea
Topological chiral homology is a generalization of Hochschild homology. Where Hochschild homology is given by (∞,1)-colimits of functors constant on an ∞\infty-algebra over a diagram that is an ∞-groupoid, topological chiral homology is given by colimits of constant functors over (∞,1)-categories of open subsets of a manifold.
This generalizes the concept of chiral homology by Beilinson-Drinfeld.
Definition
For the moment see the section Topological chiral homology at the entry on Hochschild homology.
The notion of topological chiral homology should be closely related to that of
and be related to concepts in
- AQFT.
Other related concepts
References
A quick definition and comments on its relation to FQFT are in section 4.1 of
Technical details are in section 3 of
which meanwhile has becomes part of section 5 of
Last revised on July 6, 2013 at 00:35:58. See the history of this page for a list of all contributions to it.