2018/01/18 by Alex Pieloch, Pieloch, Alex
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1801.06210
openalex publication_date 2018/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these results by defining a new complex associated to a not necessarily orientable surface with boundary called the ABC-complex. This complex encodes the intersection patterns of isotopy classes of essential simple arcs, boundary components, and essential simple closed curves. We show that this complex is homotopy equivalent to an infinite wedge of spheres; its dimension is dependent on the topological type of the surface.