2003/04/13 by Martin Markl, Markl, Martin
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.AT #math.QA
paper · pdf · doi:10.48550/arxiv.math/0304161
A historical overview added and the main results clearly formulated. 40 pages
openalex publication_date 2003/04/13 · arxiv created 2010/09/24 · arxiv updated 2010/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a cofibrant E-infty operad generated by the Fox-Neuwirth cells of the configuration space of points in the Euclidean space. We show that, below the `critical dimensions' in which `bad cells' exist, this operad is modeled by the geometry of the Fulton-MacPherson compactification of this configuration space. We analyze the Tamarkin bad cell and calculate the differential of the corresponding generator. We also describe a simpler, four-dimensional bad cell. We finish the paper by proving an auxiliary result giving a characterization, over integers, of free Lie algebras.