Homotopy invariants for $\overline{\mathcal{M}}_{0,n}$ via Koszul duality
Algebraic Topology
2022-03-30 v3 K-Theory and Homology
Abstract
We show that the integral cohomology rings of the moduli spaces of stable rational marked curves are Koszul. This answers an open question of Manin. Using the machinery of Koszul spaces developed by Berglund, we compute the rational homotopy Lie algebras of those spaces, and obtain some estimates for Betti numbers of their free loop spaces in case of torsion coefficients. We also prove and conjecture some generalisations of our main result.
Keywords
Cite
@article{arxiv.1902.06318,
title = {Homotopy invariants for $\overline{\mathcal{M}}_{0,n}$ via Koszul duality},
author = {Vladimir Dotsenko},
journal= {arXiv preprint arXiv:1902.06318},
year = {2022}
}
Comments
26 pages, much more detailed version, (most) misprints corrected