Factorization Homology of Polynomial Algebras

TL;DR

This paper introduces a novel method for computing the factorization homology of polynomial algebras on manifolds, utilizing graph complexes and explicit morphisms to enable algebraic twisting and deformations.

Contribution

It presents a new approach to calculating factorization homology using graph complexes and explicit morphisms, allowing for algebraic twists with Maurer-Cartan elements.

Findings

Computed factorization homology of polynomial algebras on manifolds

Developed a graph complex model for the calculation

Enabled algebraic twisting via Maurer-Cartan elements

Abstract

We compute the factorization homology of a polynomial algebra over a compact and closed manifold with trivialized tangent bundle up to weak equivalence in a new way. This calculation is based on the model of a graph complex and an explicit morphism into the codomain, which makes it possible to twist the algebra with a Maurer-Cartan element and potentially apply other deformations.