Volume 21, issue 5 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Brown's moduli spaces of curves and the gravity operad

Clément Dupont and Bruno Vallette

Geometry & Topology 21 (2017) 2811–2850
Bibliography
1 J Alm, A universal A-infinity structure on Batalin–Vilkovisky algebras with multiple zeta value coefficients, preprint (2015) arXiv:1501.02916
2 J Alm, D Petersen, Brown’s dihedral moduli space and freedom of the gravity operad, preprint (2015) arXiv:1509.09274
3 V I Arnol’d, The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227 MR0242196
4 J Bergström, F Brown, Inversion of series and the cohomology of the moduli spaces 0,nδ, from: "Motives, quantum field theory, and pseudodifferential operators" (editors A Carey, D Ellwood, S Paycha, S Rosenberg), Clay Math. Proc. 12, Amer. Math. Soc. (2010) 119 MR2762527
5 F C S Brown, Multiple zeta values and periods of moduli spaces 𝔐0,n, Ann. Sci. Éc. Norm. Supér. 42 (2009) 371 MR2543329
6 P Deligne, Théorie de Hodge, I, from: "Actes du Congrès International des Mathématiciens", Gauthier-Villars (1971) 425 MR0441965
7 P Deligne, Théorie de Hodge, II, Inst. Hautes Études Sci. Publ. Math. 40 (1971) 5 MR0498551
8 P Deligne, Théorie de Hodge, III, Inst. Hautes Études Sci. Publ. Math. 44 (1974) 5 MR0498552
9 S L Devadoss, Tessellations of moduli spaces and the mosaic operad, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 91 MR1718078
10 V Dotsenko, Freeness theorems for operads via Gröbner bases, from: "Operads 2009" (editors J L Loday, B Vallette), Sémin. Congr. 26, Soc. Math. France (2013) 61 MR3203367
11 V Dotsenko, A Khoroshkin, Gröbner bases for operads, Duke Math. J. 153 (2010) 363 MR2667136
12 C Dupont, Purity, formality, and arrangement complements, Int. Math. Res. Not. 2016 (2016) 4132 MR3544631
13 E Getzler, Two-dimensional topological gravity and equivariant cohomology, Comm. Math. Phys. 163 (1994) 473 MR1284793
14 E Getzler, Operads and moduli spaces of genus 0 Riemann surfaces, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 199 MR1363058
15 E Getzler, M M Kapranov, Cyclic operads and cyclic homology, from: "Geometry, topology, & physics" (editor S T Yau), Conf. Proc. Lecture Notes Geom. Topology IV, Int. Press (1995) 167 MR1358617
16 V Ginzburg, M Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203 MR1301191
17 A B Goncharov, Y I Manin, Multiple ζ–motives and moduli spaces 0,n, Compos. Math. 140 (2004) 1 MR2004120
18 S Keel, Intersection theory of moduli space of stable n–pointed curves of genus zero, Trans. Amer. Math. Soc. 330 (1992) 545 MR1034665
19 M Kim, Weights in cohomology groups arising from hyperplane arrangements, Proc. Amer. Math. Soc. 120 (1994) 697 MR1179589
20 F F Knudsen, The projectivity of the moduli space of stable curves, II : The stacks Mg,n, Math. Scand. 52 (1983) 161 MR702953
21 G I Lehrer, The l–adic cohomology of hyperplane complements, Bull. London Math. Soc. 24 (1992) 76 MR1139062
22 J L Loday, B Vallette, Algebraic operads, 346, Springer (2012) MR2954392
23 C A M Peters, J H M Steenbrink, Mixed Hodge structures, 52, Springer (2008) MR2393625
24 D Quillen, Rational homotopy theory, Ann. of Math. 90 (1969) 205 MR0258031
25 M Saito, Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci. 24 (1988) 849 MR1000123
26 P Salvatore, R Tauraso, The operad Lie is free, J. Pure Appl. Algebra 213 (2009) 224 MR2467399
27 B Z Shapiro, The mixed Hodge structure of the complement to an arbitrary arrangement of affine complex hyperplanes is pure, Proc. Amer. Math. Soc. 117 (1993) 931 MR1131042