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

[41] The φ→γK0(K)over-bar0 decay
Oller, JA
PHYSICS LETTERS B, 1998, 426 (1-2) : 7 - 11
[42] D0-(D)over-bar0 oscillations
Eroshenko, Yu N.
PHYSICS-USPEKHI, 2013, 56 (04) : 426 - 426
[43] The φ→K0(K)over-bar0γ decay
Escribano, R.
EUROPEAN PHYSICAL JOURNAL A, 2007, 31 (04): : 454 - 457
[44] D0-(D)over-bar0 mixing
Ligeti, Z
HEAVY FLAVOR PHYSICS, 2002, 618 : 298 - 309
[45] (B)over-bar0 decays to D(*)0η and D(*)0η′
Deandrea, A
Polosa, AD
EUROPEAN PHYSICAL JOURNAL C, 2002, 22 (04): : 677 - 681
[46] Study of (B)over-bar0→D(*)0π+π- decays
Satpathy, A
Abe, K
Abe, R
Abe, T
Adachi, I
Aihara, H
Akatsu, M
Asano, Y
Aso, T
Aushev, T
Bakich, AM
Ban, Y
Bay, A
Bedny, I
Behera, PK
Bondar, A
Bozek, A
Bracko, M
Browder, TE
Casey, BCK
Chang, P
Chao, Y
Chen, KF
Cheon, BG
Chistov, R
Choi, SK
Choi, Y
Choi, Y
Danilov, M
Dong, LY
Eidelman, S
Eiges, V
Fukunaga, C
Gabyshev, N
Garmash, A
Gershon, T
Golob, B
Haba, J
Hara, T
Hastings, NC
Hayashii, H
Hazumi, M
Higuchi, I
Hinz, L
Hokuue, T
Hou, WS
Huang, HC
Igaki, T
Igarashi, Y
Iijima, T
PHYSICS LETTERS B, 2003, 553 (3-4) : 159 - 166
[47] Decay of the J/ψ to Σ0(Σ)over-bar0 final state
Bai, JZ
Yong, B
Bian, JG
Chang, JF
Chen, AD
Chen, HF
Chen, HS
Chen, JC
Chen, XD
Chen, YB
Cheng, BS
Chi, SP
Chu, YP
Cui, XZ
Dai, YS
Dong, LY
Du, ZZ
Fu, HY
Fu, LP
Gao, CS
Gu, SD
Guo, ZJ
Guo, YN
Han, SW
Han, Y
He, JT
He, J
He, KL
He, M
He, X
Heng, YK
Hong, T
Hu, GY
Hu, HM
Hu, QH
Hu, T
Huang, GS
Huang, XP
Huang, YZ
Ji, XB
Jiang, CH
Yan, J
Ke, ZJ
Lai, YF
Li, D
Li, HB
Li, HH
Li, JC
Li, J
Li, PQ
HIGH ENERGY PHYSICS AND NUCLEAR PHYSICS-CHINESE EDITION, 2002, 26 (02): : 93 - 99
[48] Evidence of a structure in (K)over-bar0Λc+ consistent with a charged Ξc(2930)+, and updated measurement of (B)over-bar0 → (K)over-bar0Λc+ (Λ)over-barc- at Belle
Li, Y. B.
Shen, C. P.
Adachi, I.
Aihara, H.
Al Said, S.
Asner, D. M.
Aushev, T.
Ayad, R.
Babu, V.
Badhrees, I.
Bahinipati, S.
Ban, Y.
Bansal, V.
Behera, P.
Beleno, C.
Bhardwaj, V.
Bhuyan, B.
Biswal, J.
Bobrov, A.
Bozek, A.
Bracko, M.
Browder, T. E.
Cao, L.
Cervenkov, D.
Chang, P.
Chekelian, V.
Chen, A.
Cheon, B. G.
Chilikin, K.
Cho, K.
Choi, S. -K.
Choi, Y.
Choudhury, S.
Cinabro, D.
Cunliffe, S.
Dash, N.
Di Carlo, S.
Dingfelder, J.
Dolezal, Z.
Dong, T. V.
Drasal, Z.
Eidelman, S.
Epifanov, D.
Fast, J. E.
Fulsom, B. G.
Garg, R.
Gaur, V.
Gabyshev, N.
Garmash, A.
Gelb, M.
EUROPEAN PHYSICAL JOURNAL C, 2018, 78 (11):
[49] Effective curves on (M)over-bar0,n from group actions
Moon, Han-Bom
Swinarski, David
MANUSCRIPTA MATHEMATICA, 2015, 147 (1-2) : 239 - 268
[50] Two-dimensional cycle classes on (M)over-bar0,n
Ramadas, Rohini
Silversmith, Rob
MATHEMATISCHE ZEITSCHRIFT, 2022, 301 (04) : 3713 - 3726

← 1 2 3 4 5 →