Homotopy invariants for ($)over-bar0, n via Koszul duality

被引：6
|
作者：
Dotsenko, Vladimir [1 ,2 ]
机构：
[1] Univ Strasbourg, Inst Rech Math Avancee, UMR 7501, 7 Rue Rene Descartes, F-67000 Strasbourg, France
[2] CNRS, 7 Rue Rene Descartes, F-67000 Strasbourg, France
来源：
INVENTIONES MATHEMATICAE | 2022年 / 228卷 / 01期
关键词：
MODULI SPACE; TORIC VARIETIES; CYCLIC HOMOLOGY; POINTED CURVES; STABLE CURVES; BETTI NUMBERS; COHOMOLOGY; SERIES; OPERADS; RING;
D O I：
10.1007/s00222-021-01081-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the integer 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.
引用
收藏
页码：77 / 106
页数：30
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