Manifoldic homology and Chern-Simons formalism

TL;DR

This paper constructs a morphism linking homology of homotopy Lie algebras to topological chiral homology for n-manifolds, advancing the mathematical foundation of perturbative Chern-Simons theory.

Contribution

It introduces a new morphism connecting homology of $e_n$-algebras to topological chiral homology, crucial for Chern-Simons formalism.

Findings

Defines a morphism from homology of homotopy Lie algebra to topological chiral homology.

Establishes a foundational link relevant for perturbative Chern-Simons theory.

Provides a mathematical framework for future research in topological quantum field theories.

Abstract

The aim of this note is to define for any $e_n$-algebra $A$ and a compact parallelizable n-manifold $M$ without borders a morphism from the homology of homotopy Lie algebra $A[n-1]$ to the topological chiral homology of $M$ with coefficients in $A$. This map plays a crucial role in the perturbative Chern-Simons theory.