The (Co)homology of the Deligne-Mumford Moduli Spaces of Marked Rational Curves

2024/04/01 by Zinger, Aleksey
#14H10 #17A30 #17A42 #18C40 #37K10 #53D45 #81T40 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2404.00839

Abstract

This informal note collects key results and open problems on the (co)homology of the Deligne-Mumford moduli spaces of real marked rational curves. The open problems are both of topological nature, aiming to investigate the (co)homology of these spaces further, and of algebraic nature, aiming to describe the structure of the homology of these spaces in operad-like terms.

Related

• Blowdowns of the Deligne-Mumford Spaces of Real Rational Curves
• The Cohomology Ring of the Deligne-Mumford Moduli Space of Real Rational Curves with Conjugate Marked Points
• Rational curves on the compactified moduli space of rational curves with marked points
• Notes on the construction of the moduli space of curves
• An analytic construction of the Deligne-Mumford compactification of the moduli space of curves