2015/04/15 by Ayala, David, Francis, John, Rozenblyum, Nick
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1504.04007
We construct a pairing, which we call factorization homology, between framed manifolds and higher categories. The essential geometric notion is that of a vari-framing of a stratified manifold, which is a framing on each stratum together with a coherent system of compatibilities of framings along links between strata. Our main result constructs labeling systems on disk-stratified vari-framed n-manifolds from (∞,n)-categories. These (∞,n)-categories, in contrast with the literature to date, are not required to have adjoints. This allows the following conceptual definition: the factorization homology ∫MC of a framed n-manifold M with coefficients in an (∞,n)-category C is the classifying space of \cC-labeled disk-stratifications over M.