2020/06/01 by Foling Zou, Zou, Foling · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2008.08234
openalex publication_date 2020/06/01 · openalex created_date 2020/08/24 · openalex updated_date 2026/08/01
Factorization homology is a homology theory on manifolds with coefficients in suitable En-algebras. In this paper, we use the minimal categorical background and maximal concreteness to study equivariant factorization homology in the V-framed case. We work with a finite group G and an n-dimensional orthogonal G-representation V. The main results are: \beginenumerate \item We construct a GTop-enriched category Mfld^frVn. Its objects are V-framed G-manifolds of dimension n. The endomorphism operad of the object V is equivalent to the little V-disk operad. \item With this category, we define the equivariant factorization homology ∫MA by a monadic bar construction. \item We prove the nonabelian Poincar'e duality theorem using a geometrically-seen scanning map, which establishes a weak G-equivalence between ∫MA and Map_*(M+, BVA). \endenumerate Here, M is a V-framed manifold, and M+ is its one-point compactification. In the language of Guillou-May \citeGM17, the coefficient A is an algebra over the little V-disks operad and BVA is the V-fold deloop of A.