The action of S_n on the cohomology of M_0,n(R)

2006/01/24 by Eric M. Rains, Rains, Eric M. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0601573

openalex publication_date 2006/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In recent work (math/0507514) by Etingof, Henriques, Kamnitzer, and the author, a presentation and explicit basis was given for the rational cohomology of the real locus M_0,n(\RR) of the moduli space of stable genus 0 curves with n marked points. We determine the graded character of the action of S_n on this space (induced by permutations of the marked points), both in the form of a plethystic formula for the cycle index, and as an explicit product formula for the value of the character on a given cycle type.

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• FA-modules of holomorphic forms on M_g,n

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