Volume 9, issue 3 (2009)

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Cohomology theories for homotopy algebras and noncommutative geometry

Alastair Hamilton and Andrey Lazarev

Algebraic & Geometric Topology 9 (2009) 1503–1583
Bibliography
1 M Alexandrov, A Schwarz, O Zaboronsky, M Kontsevich, The geometry of the master equation and topological quantum field theory, Internat. J. Modern Phys. A 12 (1997) 1405 MR1432574
2 M Barr, Harrison homology, Hochschild homology and triples, J. Algebra 8 (1968) 314 MR0220799
3 X Z Cheng, E Getzler, Transferring homotopy commutative algebraic structures, J. Pure Appl. Algebra 212 (2008) 2535 MR2440265
4 J Conant, K Vogtmann, On a theorem of Kontsevich, Algebr. Geom. Topol. 3 (2003) 1167 MR2026331
5 A Connes, Noncommutative geometry, Academic Press (1994) MR1303779
6 A Fialowski, M Penkava, Deformation theory of infinity algebras, J. Algebra 255 (2002) 59 MR1935035
7 M Gerstenhaber, The cohomology structure of an associative ring, Ann. of Math. $(2)$ 78 (1963) 267 MR0161898
8 M Gerstenhaber, S D Schack, A Hodge-type decomposition for commutative algebra cohomology, J. Pure Appl. Algebra 48 (1987) 229 MR917209
9 E Getzler, Lie theory for nilpotent $L_\infty$–algebras arXiv:math.AT/0404003
10 E Getzler, A Darboux theorem for Hamiltonian operators in the formal calculus of variations, Duke Math. J. 111 (2002) 535 MR1885831
11 E Getzler, J D S Jones, Operads, homotopy algebra, and iterated integrals for double loop spaces arXiv:hep-th/9403055
12 E Getzler, J D S Jones, $A_\infty$–algebras and the cyclic bar complex, Illinois J. Math. 34 (1990) 256 MR1046565
13 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
14 V Ginzburg, Non-commutative symplectic geometry, quiver varieties, and operads, Math. Res. Lett. 8 (2001) 377 MR1839485
15 W M Goldman, J J Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Inst. Hautes Études Sci. Publ. Math. (1988) 43 MR972343
16 A Hamilton, On the classification of Moore algebras and their deformations, Homology Homotopy Appl. 6 (2004) 87 MR2061569
17 A Hamilton, A super-analogue of Kontsevich's theorem on graph homology, Lett. Math. Phys. 76 (2006) 37 MR2223762
18 A Hamilton, A Lazarev, Characteristic classes of $A_\infty$–algebras, J. Homotopy Relat. Struct. 3 (2008) 65 MR2395368
19 D K Harrison, Commutative algebras and cohomology, Trans. Amer. Math. Soc. 104 (1962) 191 MR0142607
20 V Hinich, Descent of Deligne groupoids, Internat. Math. Res. Notices (1997) 223 MR1439623
21 T V Kadeishvili, The algebraic structure in the homology of an $A(\infty )$–algebra, Soobshch. Akad. Nauk Gruzin. SSR 108 (1982) MR720689
22 M Kapranov, Noncommutative geometry based on commutator expansions, J. Reine Angew. Math. 505 (1998) 73 MR1662244
23 C Kassel, Quantum groups, Graduate Texts in Math. 155, Springer (1995) MR1321145
24 B Keller, Introduction to $A$–infinity algebras and modules, Homology Homotopy Appl. 3 (2001) 1 MR1854636
25 M Kontsevich, Formal (non)commutative symplectic geometry, from: "The Gel$'$fand Mathematical Seminars, 1990–1992" (editors L Corwin, I Gel′fand, J Lepowsky), Birkhäuser (1993) 173 MR1247289
26 M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)", Progr. Math. 120, Birkhäuser (1994) 97 MR1341841
27 M Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003) 157 MR2062626
28 M Kontsevich, A L Rosenberg, Noncommutative smooth spaces, from: "The Gelfand Mathematical Seminars, 1996–1999" (editors I M Gelfand, V S Retakh), Birkhäuser (2000) 85 MR1731635
29 M Kontsevich, A L Rosenberg, Noncommutative spaces and flat descent, MPIM Preprint 2004-36, Max-Planck Insitut für Mathematik (2004)
30 I Kříž, J P May, Operads, algebras, modules and motives, Astérisque (1995) MR1361938
31 A Lazarev, Hochschild cohomology and moduli spaces of strongly homotopy associative algebras, Homology Homotopy Appl. 5 (2003) 73 MR1989615
32 J L Loday, Cyclic homology, Grund. der Math. Wissenschaften 301, Springer (1998) MR1600246
33 M Markl, A cohomology theory for $A(m)$–algebras and applications, J. Pure Appl. Algebra 83 (1992) 141 MR1191090
34 M Markl, Homotopy algebras are homotopy algebras, Forum Math. 16 (2004) 129 MR2034546
35 M Markl, S Shnider, J Stasheff, Operads in algebra, topology and physics, Math. Surveys and Monogr. 96, Amer. Math. Soc. (2002) MR1898414
36 J Milles, Andre–Quillen cohomology of algebras over an operad arXiv:0806.4405
37 T Natsume, S D Schack, A decomposition for the cyclic cohomology of a commutative algebra, J. Pure Appl. Algebra 61 (1989) 273 MR1027747
38 M Penkava, A Schwarz, $A_\infty$ algebras and the cohomology of moduli spaces, from: "Lie groups and Lie algebras: E B Dynkin's Seminar" (editors S G Gindikin, E B Vinberg), Amer. Math. Soc. Transl. Ser. 2 169, Amer. Math. Soc. (1995) 91 MR1364455
39 A Polishchuk, Extensions of homogeneous coordinate rings to $A_\infty$–algebras, Homology Homotopy Appl. 5 (2003) 407 MR2072342
40 D Quillen, Rational homotopy theory, Ann. of Math. $(2)$ 90 (1969) 205 MR0258031
41 M Schlessinger, J Stasheff, Deformation theory and rational homotopy type, Preprint
42 J Stasheff, Homotopy associativity of $H$–spaces. I, Trans. Amer. Math. Soc. 108 (1963) 275 MR0158400
43 J Stasheff, Homotopy associativity of $H$–spaces. II, Trans. Amer. Math. Soc. 108 (1963) 293 MR0158400
44 J Stasheff, The intrinsic bracket on the deformation complex of an associative algebra, J. Pure Appl. Algebra 89 (1993) 231 MR1239562
45 D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977) MR0646078
46 A A Voronov, Notes on universal algebra, from: "Graphs and patterns in mathematics and theoretical physics" (editors M Lyubich, L Takhtajan), Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 81 MR2131012
47 B Zwiebach, Closed string field theory: quantum action and the Batalin–Vilkovisky master equation, Nuclear Phys. B 390 (1993) 33 MR1203476