2020/05/05 by Pierre Clavier, Clavier, Pierre J., Loïc Foissy +3
Mathematics · #18M85 #46E99 #47G30 #Advanced Operator Algebra Research #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2005.02115
openalex publication_date 2020/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We assign generalised convolutions (resp. traces) to graphs whose edges are decorated by smooth kernels (resp. smoothing operators) on a closed manifold. To do so, we introduce the concept of TraPs (Traces and Permutations), which roughly correspond to ProPs (Products and Permutations) without vertical concatenation and equipped with families of generalised partial traces. They can be equipped with a ProP structure in deriving vertical concatenation from the partial traces and we relate TraPs to wheeled ProPs first introduced by Merkulov. We further build their free object and give precise proofs of universal properties of ProPs and TraPs.