Stability of the Rational Homotopy Type of Moduli Spaces

1997/08/22 by Alexander A. Voronov, Voronov, Alexander A.
Computer Science · Mathematics · #14H10 (Primary) 32G15 #55P62 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #alg-geom #math.AG #msc:14H10 #msc:32G15 #msc:55P62

paper · pdf · doi:10.48550/arxiv.alg-geom/9708019

7 pages, 1 figure

arxiv created 1997/08/22 · openalex publication_date 1997/08/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for g > 2k+2 the k-rational homotopy type of the moduli space M_g,n of algebraic curves of genus g with n punctures is independent of g, and the space M_g,n is k-formal. This implies the existence of a limiting rational homotopy type of M_g,n as g goes to infinity and the formality of it.

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