[1] Alekseev, A., Enriquez, B., Torossian, C.:
Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations. Publications Mathématiques de l’IHéS 112 143-189 arXiv:0903.4067
DOI 10.1007/s10240-010-0029-4 |
MR 2737979
[3] Alekseev, A., Rossi, C. A., Torossian, C., Willwacher, T.:
Logarithms and deformation quantization. Inventiones mathematicae 206 1 1-28 arXiv:1401.3200
DOI 10.1007/s00222-016-0647-7 |
MR 3556523
[6] Alexandrov, M., Schwarz, A., Zaboronsky, O., Kontsevich, M.: The Geometry of the master equation and topological quantum field theory. Int. J. Mod. Phys. A 12 1405 arXiv:hep-th/9502010
[7] Alm, J.: Universal algebraic structures on polyvector fields. Ph.D. Thesis, Stockholm University, Faculty of Science, Department of Mathematics
[8] Alm, J., Merkulov, S.:
Grothendieck-Teichmueller group and Poisson cohomologies. Journal of Noncommutative Geometry 9 1 185-214 arXiv:1203.5933
DOI 10.4171/jncg/191 |
MR 3337958
[9] Arnal, D., Amar, N. B., Masmoudi, M.: Cohomology of Good Graphs and Kontsevich Linear State Products. Letters in Mathematical Physics 48 4 291-306
[11] Bar-Natan, D., McKay, B.: Graph cohomology-an overview and some computations. Unpublished
[12] Batalin, I. A., Vilkovisky, G. A.: Gauge Algebra and Quantization. Physics Letters B 102 1 27-31
[13] Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., Sternheimer, D.: Deformation Theory and Quantization. 1. Deformations of Symplectic Structures. Annals Phys. 111 1 61-110
[16] Bouisaghouane, A., Kiselev, A. V.: Do the Kontsevich tetrahedral flows preserve or destroy the space of Poisson bi-vectors?. Journal of Physics: Conf.Series 804 Paper 012008 arXiv:1609.06677
[19] Buring, R., Kiselev, A. V.: The orientation morphism: from graph cocycles to deformations of Poisson structures. Journal of Physics: Conference Series 1194 Paper 012017 1-10 arXiv:1811.07878
[21] Buring, R., Kiselev, A. V., Rutten, N. J.: Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus. Journal of Physics: Conf. Series 965 Paper 012010 arXiv:1710.02405
[22] Buring, R., Kiselev, A. V., Rutten, N. J.:
Poisson Brackets Symmetry from the Pentagon-Wheel Cocycle in the Graph Complex. Physics of Particles and Nuclei 49 5 924-928 arXiv:1712.05259
DOI 10.1134/S1063779618050118
[23] Bursztyn, H., Dolgushev, V. A., Waldmann, S.:
Morita equivalence and characteristic classes of star products. Journal für die reine und angewandte Mathematik 2012 662 95-163 arXiv:0909.4259
MR 2876262
[25] Cattaneo, A. S., Felder, G.: A Path integral approach to the Kontsevich quantization formula. Commun. Math. Phys. 212 591 arXiv:math/9902090
[26] Cattaneo, A. S., Felder, G.:
On the AKSZ formulation of the Poisson sigma model. Letters in Mathematical Physics 56 163 arXiv:math/0102108
MR 1854134
[28] Cattaneo, A., Keller, B., Torossian, C., Bruguières, A.:
Déformation, Quantification, Théorie de Lie. Panoramas et Synthèses SMF 20
MR 2274222
[31] Courant, T., Weinstein, A.: Beyond Poisson structures. in Actions hamiltoniennes de groupes. Troisième théorème de Lie (Lyon), Travaux en Cours 27 Hermann Paris 39-49
[33] Culler, M., Vogtmann, K.:
Moduli of graphs and automorphisms of free groups. Inventiones mathematicae 84 1 91-119
DOI 10.1007/BF01388734
[34] Dito, G.:
Kontsevich star-product on the dual of a Lie algebra. Letters in Mathematical Physics 48 4 307-322 arXiv:math/9905080
DOI 10.1023/A:1007643618406
[35] Dolgushev, V. A.:
Erratum to: A Proof of Tsygan’s Formality Conjecture for an Arbitrary Smooth Manifold (2007). arXiv:math/0703113
MR 2717256
[36] Dolgushev, V. A.:
Stable Formality Quasi-isomorphisms for Hochschild Cochains. Mémoires de la Société Mathématique de France 168 SMF arXiv:1109.6031
MR 4234594
[37] Dolgushev, V. A.:
A Formality quasi-isomorphism for Hochschild cochains over rationals can be constructed recursively. International Mathematics Research Notices 18 5729-5785 arXiv:1306.6733
MR 3862118
[38] Dolgushev, V. A., Paljug, B.:
Tamarkin’s construction is equivariant with respect to the action of the Grothendieck-Teichmueller group. Journal of Homotopy and Related Structures 11 3 503-552 arXiv:1402.7356
DOI 10.1007/s40062-015-0115-x |
MR 3542096
[39] Dolgushev, V. A., Rogers, C. L.:
Notes on Algebraic Operads, Graph Complexes, and Willwacher’s Construction. Contemporary Mathematics 583 “Mathematical Aspects of Quantization” arXiv:1202.2937
MR 3013092
[40] Dolgushev, V. A., Rogers, C. L.:
The cohomology of the full directed graph complex. Algebras and Representation Theory 1-45 arXiv:1711.04701
MR 4109144
[41] Dolgushev, V. A., Rogers, C. L., Willwacher, T.:
Kontsevich’s graph complex, GRT, and the deformation complex of the sheaf of polyvector fields. Annals of Mathematics Second Series 182 3 855-943 arXiv:1211.4230
MR 3418532
[42] Dolgushev, V. A., Schneider, G. E.:
When can a formality quasi-isomorphism over rationals be constructed recursively?. Journal of Pure and Applied Algebra 223 5 2145-2172 arXiv:1610.04879
DOI 10.1016/j.jpaa.2018.07.012 |
MR 3906544
[43] Dorfman, I. Y.:
Dirac structures of integrable evolution equations. Physics Letters A 125 5 240-246 Dirac structures and integrability of nonlinear evolution equations Nonlinear science : theory and applications John Wiley & Sons Ltd., Chichester
DOI 10.1016/0375-9601(87)90201-5
[44] Drinfel’d, V. G.: On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(ℚ-bar/ℚ). Algebra i Analiz 2 4 149-181 ; Leningrad Math. J. 2 4 829-860
[45] Esposito, C., Stapor, P., Waldmann, S.:
Convergence of the Gutt Star Product. Journal of Lie Theory 27 2 579-622 arXiv:1509.09160
MR 3589272
[46] Etingof, P., Kazhdan, D.: Quantization of Lie bialgebras, I. Selecta Mathematica 2 1 1-41 arXiv:q-alg/9506005
[47] Felder, G., Willwacher, T.:
On the (ir)rationality of Kontsevich weights. International Mathematics Research Notices 2010 4 701-716 arXiv:0808.2762
MR 2595009
[48] Fresse, B.:
Homotopy of operads & Grothendieck-Teichmüller groups. Mathematical Surveys and Monographs 217 1236pp
MR 3616816
[49] Fresse, B., Turchin, V., Willwacher, T.:
The rational homotopy of mapping spaces of E_(n) operads (2017). arXiv:1703.06123
MR 3870769
[51] Gerstenhaber, M.:
The Cohomology Structure of an Associative Ring. Annals of Mathematics Second Series 78 2 267-288
DOI 10.2307/1970343
[52] Getzler, E., Kapranov, M. M.:
Modular operads. Compositio Mathematica 110 1 65-125 arXiv:dg-ga/9408003
DOI 10.1023/A:1000245600345
[53] Goldman, W. M., Millson, J. J.:
The deformation theory of representations of fundamental groups of compact Kähler manifolds. Publications Mathématiques de l’IHéS 67 43-96
DOI 10.1007/BF02699127
[54] Gorbounov, V., Malikov, F., Schechtman, V.:
Gerbes of chiral differential operators. II. Vertex algebroids. Inventiones mathematicae 155 605-680 arXiv:math/0003170
DOI 10.1007/s00222-003-0333-4 |
MR 2038198
[55] Gorbounov, V., Malikov, F., Schechtman, V.:
Gerbes of chiral differential operators. III. C. Duval, V. Ovsienko, L. Guieu (eds) The Orbit Method in Geometry and Physics: In Honor of A.A. Kirillov. Progress in Mathematics 213 73–100 Birkhäuser, Boston, MA. arXiv:math/0005201
MR 1995376
[57] Grothendieck, A.: Esquisse d’un Programme. London Math. Soc. Lect. Note Ser. 1 7-48
[60] Gutt, S.:
An explicit *-product on the cotangent bundle of a Lie group. Letters in Mathematical Physics 7 3 249-258
DOI 10.1007/BF00400441
[61] Hinich, V.:
Tamarkin’s proof of Kontsevich formality theorem. Forum Mathematicum 15 4 591-614 arXiv:math/0003052
MR 1978336
[62] Hitchin, N.:
Generalized Calabi-Yau manifolds. Quarterly Journal of Mathematics 54 3 arXiv:math/0209099
MR 2013140
[63] Hofman, C., Park, J. S.: Topological open membranes (2002). arXiv:hep-th/0209148
[64] Hofman, C., Park, J. S.:
BV quantization of topological open membranes. Commun. Math. Phys. 249 2 249-271 arXiv:hep-th/0209214
MR 2080953
[65] Ikeda, N.: Two-dimensional gravity and nonlinear gauge theory. Annals Phys. 235 435 arXiv:hep-th/9312059
[66] Ikeda, N.:
Deformation of BF theories, topological open membrane and a generalization of the star deformation. JHEP 0107 037 arXiv:hep-th/0105286
MR 1850860
[67] Ikeda, N.:
Chern–Simons gauge theory coupled with BF theory. Int. J. Mod. Phys. A 18 2689 arXiv:hep-th/0203043
MR 1985761
[68] Ikeda, N., Izawa, K. I.: General form of dilaton gravity and nonlinear gauge theory. Prog. Theor. Phys. 90 237 arXiv:hep-th/9304012
[69] Ikeda, N., Uchino, K.:
QP-Structures of Degree 3 and 4D Topological Field Theory. Commun. Math. Phys. 303 317 arXiv:1004.0601
MR 2782617
[70] Jost, C.:
Globalizing L-infinity automorphisms of the Schouten algebra of polyvector fields. Differential Geometry and its Applications 31 2 239-247 arXiv:1201.1392
DOI 10.1016/j.difgeo.2012.12.002 |
MR 3032646
[71] Jurco, B., Vysoky, J.:
Courant Algebroid Connections and String Effective Actions. Noncommutative Geometry and Physics 4 211-265 arXiv:1612.01540
MR 3674835
[72] Kathotia, V.:
Kontsevich’s Universal Formula for Deformation Quantization and the Campbell-Baker-Hausdorff Formula, I. International Journal of Mathematics 11 04 523-551 arXiv:math/9811174
DOI 10.1142/S0129167X0000026X
[74] Keller, F., Waldmann, S.:
Deformation Theory of Courant Algebroids via the Rothstein Algebra. Journal of Pure and Applied Algebra 219 8 3391-3426 arXiv:0807.0584
DOI 10.1016/j.jpaa.2014.12.002 |
MR 3320226
[76] Kiselev, A. V.: Open problems in the Kontsevich graph construction of Poisson bracket symmetries. Journal of Physics: Conference Series 1416 Issue 1 012018 1184-1214 arXiv:1910.05844
[77] Kiselev, A. V., Buring, R.:
The Kontsevich graph orientation morphism revisited. Banach Center Publications 123 123-139 arXiv:1904.13293
DOI 10.4064/bc123-5 |
MR 4276046
[78] Klimčik, C., Strobl, T.:
WZW - Poisson manifolds. J. Geom. Phys. 43 341 arXiv:math/0104189
MR 1929911
[79] Kneissler, J.:
On spaces of connected graphs I: Properties of Ladders. Proc. Internat. Conf. “Knots in Hellas ’98”, Series on Knots and Everything 24 252-273 arXiv:math/0301018
MR 1865711
[80] Kneissler, J.:
On spaces of connected graphs II: Relations in the algebra Lambda. Journal of Knot Theory and Its Ramifications 10 5 667-674 arXiv:math/0301019
DOI 10.1142/S0218216501001074 |
MR 1839694
[81] Kneissler, J.:
On spaces of connected graphs III: The Ladder Filtration. Journal of Knot Theory and Its Ramifications 10 5 675-686 arXiv:math/0301020
DOI 10.1142/S0218216501001086 |
MR 1839695
[82] Kontsevich, M.: Feynman Diagrams and Low-Dimensional Topology. First European Congress of Mathematics Paris 97-121
[83] Kontsevich, M.: Formal (non)-commutative symplectic geometry. The Gelfand Mathematical Seminars 1990-1992 173-187
[84] Kontsevich, M.: Formality conjecture. Deformation Theory and Symplectic Geometry 20 139-156
[86] Kontsevich, M.:
Operads and Motives in Deformation Quantization. Letters in Mathematical Physics 48 35-72 arXiv:math/9904055
DOI 10.1023/A:1007555725247
[87] Kosmann-Schwarzbach, Y.:
Courant Algebroids. A Short History. SIGMA 9 014 8p. arXiv:1212.0559
MR 3033556
[88] Le, T. T. Q., Murakami, J.: Kontsevich’s integral for the Kauffman polynomial. Nagoya Mathematical Journal 142 39-65
[90] Liu, Z. J., Weinstein, A., Xu, P.: Manin triples for Lie bialgebroids. J. Diff. Geom. 45 no.3, 547 arXiv:dg-ga/9508013
[91] Loday, J. L., Vallette, B.:
Algebraic Operads. Grundlehren der mathematischen Wissenschaften 346 636p
MR 2954392
[92] Markl, M.: Cyclic operads and homology of graph complexes. J. Slovák and M. Čadek (eds.): Proceedings of the 18th Winter School “Geometry and Physics”. Circolo Matematico di Palermo, Palermo 161-170 arXiv:math/9801095
[93] Mehta, R. A.:
Supergroupoids, double structures, and equivariant cohomology. Ph.D. Thesis, University of California, Berkeley arXiv:math/0605356
MR 2709144
[94] Merkulov, S.: Exotic automorphisms of the Schouten algebra of polyvector fields (2008). arXiv:0809.2385
[96] Merkulov, S.:
Grothendieck-Teichmueller group, operads and graph complexes: a survey. Integrability, Quantization, and Geometry II. Quantum Theories and Algebraic Geometry, Proc. Sympos. Pure Math. 103 Amer. Math. Soc., Providence, RI 383-445 arXiv:1904.13097
MR 4285704
[97] Merkulov, S., Vallette, B.:
Deformation theory of representations of prop(erad)s. Journal für die reine und angewandte Mathematik 2009 634 51-106 arXiv:0707.0889
MR 2560406
[99] Morand, K.:
A Note on Multi-Oriented Graph Complexes and Deformation Quantization of Lie Bialgebroids. SIGMA 18 020 arXiv:2102.07593
MR 4395777
[100] Moyal, J. E.:
Quantum mechanics as a statistical theory. Mathematical Proceedings of the Cambridge Philosophical Society 45 1 99-124
DOI 10.1017/S0305004100000487
[101] Penner, R. C.:
The decorated Teichmüller space of punctured surfaces. Commun.Math. Phys. 113 2 299-339
DOI 10.1007/BF01223515
[102] Penner, R. C.: Perturbative series and the moduli space of Riemann surfaces. J. Differential Geom. 27 1 35-53
[103] Rossi, C. A., Willwacher, T.: P. Etingof’s conjecture about Drinfel’d associators (2014). arXiv:1404.2047
[104] Roytenberg, D.: Courant algebroids, derived brackets and even symplectic supermanifolds. Ph.D. Thesis, University of California, Berkeley arXiv:math/9910078
[105] Roytenberg, D.:
On the structure of graded symplectic supermanifolds and Courant algebroids. Contemp. Math. 315 Amer. Math. Soc. arXiv:math/0203110
MR 1958835 |
Zbl 1036.53057
[106] Roytenberg, D.:
AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories. Letters in Mathematical Physics 79 143 arXiv:hep-th/0608150
MR 2301393
[107] Rutten, N. J., Kiselev, A. V.: The defining properties of the Kontsevich unoriented graph complex. Journal of Physics: Conference Series 1194 Paper 012095 1-10 arXiv:1811.10638
[108] Schaller, P., Strobl, T.:
Poisson structure induced (topological) field theories. Mod. Phys. Lett. A 9 3129 arXiv:hep-th/9405110
Zbl 1015.81574
[110] Ševera, P.:
Quantization of Poisson families and of twisted Poisson structures. Letters in Mathematical Physics 63 2 105-113 arXiv:math/0205294
DOI 10.1023/A:1023077126186 |
MR 1978549
[111] Ševera, P., Weinstein, A.:
Poisson geometry with a 3 form background. Prog. Theor. Phys. Suppl. 144 145 arXiv:math/0107133
MR 2023853
[112] Ševera, P., Willwacher, T.:
Equivalence of formalities of the little discs operad. Duke Math. J. 160 1 175-206 arXiv:0905.1789
MR 2838354
[113] Shoikhet, B.: On the Kontsevich and the Campbell-Baker-Hausdorff deformation quantizations of a linear Poisson structure (1999). arXiv:math/9903036
[115] Tamarkin, D. E.: Another proof of M. Kontsevich formality theorem for $ℝ^(n)$ (1998). arXiv:math/9803025
[116] Tamarkin, D. E.:
Quantization of lie Bialgebras via the Formality of the operad of Little Disks. GAFA Geometric And Functional Analysis 17 2 537-604
DOI 10.1007/s00039-007-0591-1 |
MR 2322494
[118] Voronov, A. A.: Quantizing Poisson Manifolds. Perspectives on Quantization (L. A. Coburn and M. A. Rieffel (eds.) Contemp. Math. 214 AMS, Providence, RI 189-195 arXiv:q-alg/9701017
[120] Willwacher, T.:
The Homotopy Braces Formality Morphism. Duke Math. J. 165 10 1815-1964 arXiv:1109.3520
MR 3522653
[121] Willwacher, T.:
Characteristic classes in deformation quantization. International Mathematics Research Notices 2015 6538-6557 arXiv:1208.4249
DOI 10.1093/imrn/rnu136 |
MR 3384487
[123] Willwacher, T.: The Grothendieck–Teichmüller Group. Unpublished notes
[124] Willwacher, T., M.Živković, :
Multiple edges in M. Kontsevich’s graph complexes and computations of the dimensions and Euler characteristics. Adv. Math. 272 553-578 arXiv:1401.4974
DOI 10.1016/j.aim.2014.12.010 |
MR 3303240
[126] Živković, M.:
Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs. High. Struct. 4 arXiv:1703.09605
MR 4074277
[127] Živković, M.:
Multi-directed graph complexes and quasi-isomorphisms between them II: Sourced graphs. Int. Math. Res. Not. 948-1004 arXiv:1712.01203
MR 4201958