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

页码：77 / 106

页数：30

共 50 条

[31] Observation of (B)over-bar0→D0π0 and (B)over-bar0→D*0π0 -: art. no. 062001
Coan, TE
Gao, YS
Liu, F
Maravin, Y
Narsky, I
Stroynowski, R
Ye, J
Artuso, M
Boulahouache, C
Bukin, K
Dambasuren, E
Mountain, R
Skwarnicki, T
Stone, S
Wang, JC
Mahmood, AH
Csorna, SE
Danko, I
Xu, Z
Bonvicini, G
Cinabro, D
Dubrovin, M
McGee, S
Bornheim, A
Lipeles, E
Pappas, SP
Shapiro, A
Sun, WM
Weinstein, AJ
Masek, G
Paar, HP
Mahapatra, R
Morrison, RJ
Nelson, HN
Briere, RA
Chen, GP
Ferguson, T
Tatishvili, G
Vogel, H
Adam, NE
Alexander, JP
Bebek, C
Berkelman, K
Blanc, F
Boisvert, V
Cassel, DG
Drell, PS
Duboscq, JE
Ecklund, KM
Ehrlich, R
PHYSICAL REVIEW LETTERS, 2002, 88 (06) : 1 - 062001
[32] Resonant final-state interactions in D0 → (K)over-bar0η, (K)over-bar0η′ decays
El Aaoud, E
Kamal, AN
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2000, 15 (26): : 4163 - 4178
[33] Study of J/ψ and ψ(3686) → Σ(1385)0(Σ)over-bar(1385)0 and Ξ0(Ξ)over-bar0
Ablikim, M.
Achasov, M. N.
Ahmed, S.
Ai, X. C.
Albayrak, O.
Albrecht, M.
Ambrose, D. J.
Amoroso, A.
An, F. F.
An, Q.
Bai, J. Z.
Bakina, O.
Ferroli, R. Baldini
Ban, Y.
Bennett, D. W.
Bennett, J. V.
Berger, N.
Bertani, M.
Bettoni, D.
Bian, J. M.
Bianchi, F.
Boger, E.
Boyko, I.
Briere, R. A.
Cai, H.
Cai, X.
Cakir, O.
Calcaterra, A.
Cao, G. F.
Cetin, S. A.
Chai, J.
Chang, J. F.
Chelkov, G.
Chen, G.
Chen, H. S.
Chen, J. C.
Chen, M. L.
Chen, S.
Chen, S. J.
Chen, X.
Chen, X. R.
Chen, Y. B.
Chu, X. K.
Cibinetto, G.
Dai, H. L.
Dai, J. P.
Dbeyssi, A.
Dedovich, D.
Deng, Z. Y.
Denig, A.
PHYSICS LETTERS B, 2017, 770 : 217 - 225
[34] Observation of ψ (3686) →Ξ (1530)0 (Ξ)over-bar (1530)0 and Ξ (1530)0 (Ξ)over-bar0
Ablikim, M.
Achasov, M. N.
Adlarson, P.
Ahmed, S.
Albrecht, M.
Aliberti, R.
Amoroso, A.
An, M. R.
An, Q.
Bai, X. H.
Bai, Y.
Bakina, O.
Ferroli, R. Baldini
Balossino, I
Ban, Y.
Begzsuren, K.
Berger, N.
Bertani, M.
Bettoni, D.
Bianchi, F.
Bloms, J.
Bortone, A.
Boyko, I
Briere, R. A.
Cai, H.
Cai, X.
Calcaterra, A.
Cao, G. F.
Cao, N.
Cetin, S. A.
Chang, J. F.
Chang, W. L.
Chelkov, G.
Chen, D. Y.
Chen, G.
Chen, H. S.
Chen, M. L.
Chen, S. J.
Chen, X. R.
Chen, Y. B.
Chen, Z. J.
Cheng, W. S.
Cibinetto, G.
Cossio, F.
Cui, X. F.
Dai, H. L.
Dai, J. P.
Dai, X. C.
Dbeyssi, A.
de Boer, R. E.
PHYSICAL REVIEW D, 2021, 104 (09)
[35] Measurement of the absolute branching fraction of D| → (K)over-bar0e| νe via (K)over-bar0 → π0π0
Ablikim, M.
Achasov, N.
Ai, X. C.
Albayrak, O.
Albrecht, M.
Ambrose, D. J.
Amoroso, A.
An, F. F.
An, Q.
Bai, J. Z.
Ferroli, R. Baldini
Ban, Y.
Bennett, D. W.
Bennett, J. V.
Bertani, M.
Bettonin, D.
Bian, J. M.
Bianchi, F.
Boger, E.
Boyko, I.
Briere, R. A.
Cai, H.
Cai, X.
Cakir, O.
Caleaterra, A.
Cao, G. F.
Cetin, S. A.
Chang, J. F.
Chelkov, G.
Chen, G.
Chen, H. S.
Chen, H. Y.
Chen, J. C.
Chen, M. L.
Chen, S.
Chen, S. J.
Chen, X.
Chen, X. R.
Chen, Y. B.
Cheng, H. P.
Chu, X. K.
Cibinetto, G.
Dai, H. L.
Dai, J. P.
Dbeyssi, A.
Dedovich, D.
Deng, Z. Y.
Denig, A.
Denysenko, I.
Destefanis, M.
CHINESE PHYSICS C, 2016, 40 (11)
[36] Observation of B+→(K)over-bar0 K+ and B0→K0 (K)over-bar0
Aubert, B.
Bona, M.
Boutigny, D.
Couderc, F.
Karyotakis, Y.
Lees, J. P.
Poireau, V.
Tisserand, V.
Zghiche, A.
Grauges, E.
Palano, A.
Chen, J. C.
Qi, N. D.
Rong, G.
Wang, P.
Zhu, Y. S.
Eigen, G.
Ofte, I.
Stugu, B.
Abrams, G. S.
Battaglia, M.
Brown, D. N.
Button-Shafer, J.
Cahn, R. N.
Charles, E.
Gill, M. S.
Groysman, Y.
Jacobsen, R. G.
Kadyk, J. A.
Kerth, L. T.
Kolomensky, Yu. G.
Kukartsev, G.
Lynch, G.
Mir, L. M.
Orimoto, T. J.
Pripstein, M.
Roe, N. A.
Ronan, M. T.
Wenzel, W. A.
del Amo Sanchez, P.
Barrett, M.
Ford, K. E.
Harrison, T. J.
Hart, A. J.
Hawkes, C. M.
Watson, A. T.
Held, T.
Koch, H.
Lewandowski, B.
Pelizaeus, M.
PHYSICAL REVIEW LETTERS, 2006, 97 (17)
[37] Charm radiative decays with neutral mesons D0→(K)over-bar0γ, D0→(K)over-bar0η(η′)γ
Fajfer, S
Prapotnik, A
Singer, P
PHYSICS LETTERS B, 2002, 550 (1-2) : 77 - 84
[38] Model independent calculation of B((B)over-bar0 → D(*)+ τ-(ν)over-bar)/B((B)over-bar0 → D(*)+e-(ν)over-bar)
Hwang, DS
Kim, DW
EUROPEAN PHYSICAL JOURNAL C, 2000, 14 (02): : 271 - 274
[39] Homotopy properties of differential lie modules over curved coalgebras and Koszul duality
Lapin, S. V.
MATHEMATICAL NOTES, 2013, 94 (3-4) : 335 - 350
[40] Homotopy properties of differential lie modules over curved coalgebras and Koszul duality
S. V. Lapin
Mathematical Notes, 2013, 94 : 335 - 350

← 1 2 3 4 5 →