One point compactifications of configuration spaces and the self duality of the little disks operad

2023/09/28 by Connor Malin, Malin, Connor
Mathematics · #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2309.16605

openalex publication_date 2023/09/28 · openalex created_date 2023/10/01 · openalex updated_date 2026/07/28

Abstract

Using configuration space level Pontryagin--Thom constructions, we construct a simple Koszul self duality map for the little disks operad Σ^∞₊ E_n. For a framed n-manifold M, we show that a compatible self duality map exists for Σ^∞₊ E_M.

Related

• Koszul self duality of manifolds
• Koszul duality for topological E_n-operads
• A model for framed configuration spaces of points
• Poincaré/Koszul Duality for General Operads
• A Compactification of the Real Configuration Space as an Operadic Completion