2014/10/13 by Martin Markl, Markl, Martin
Mathematics · Physics and Astronomy · #18D35 #18D50 #32G15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · doi:10.48550/arxiv.1410.3414
openalex publication_date 2014/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our aim is to introduce and advocate non-Σ (non-symmetric) modular operads. While ordinary modular operads were inspired by the structure of the moduli space of stable complex curves, non-Σ modular operads model surfaces with open strings outputs. An immediate application of our theory is a short proof that the modular envelope of the associative operad is the linearization of the terminal operad in the category of non-Σ modular operads. This gives a succinct description of this object that plays an important role in open string field theory. We also sketch further perspectives of the presented approach.