1998/07/08 by Alexander A. Voronov, Voronov, Alexander A. · 2 citations
Mathematics · Physics and Astronomy · #17A30 #17A42 #18C99 (Primary) 14H10 #55P99 #81T40 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #hep-th #math.AT #math.QA #msc:14H10 #msc:17A30 #msc:17A42 #msc:18C99 #msc:55P99 #msc:81T40
paper · pdf · doi:10.48550/arxiv.math/9807037
9 pages, 2 figures
arxiv created 1998/07/08 · openalex publication_date 1998/07/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new operad, which we call the Swiss-cheese operad. It mixes naturally the little disks and the little intervals operads. The Swiss-cheese operad is related to the configuration spaces of points on the upper half-plane and points on the real line, considered by Kontsevich for the sake of deformation quantization. This relation is similar to the relation between the little disks operad and the configuration spaces of points on the plane. The Swiss-cheese operad may also be regarded as a finite-dimensional model of the moduli space of genus-zero Riemann surfaces appearing in the open-closed string theory studied recently by Zwiebach. We describe algebras over the homology of the Swiss-cheese operad.