Homotopy invariants for "Equation missing"<!-- No EquationSource Format="TEX", only image -->via Koszul duality
نویسندگان
چکیده
We show that the integral cohomology rings of moduli spaces stable rational marked curves are Koszul. This answers an open question Manin. Using machinery Koszul developed by Berglund, we compute homotopy Lie algebras those spaces, and obtain some estimates for Betti numbers their free loop in case torsion coefficients. also prove conjecture generalisations our main result.
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 2021
ISSN: ['0020-9910', '1432-1297']
DOI: https://doi.org/10.1007/s00222-021-01081-x