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Cyclic $A_\infty$ structures and Deligne's conjecture

Benjamin C Ward

Algebraic & Geometric Topology 12 (2012) 1487–1551
1 A Abbondandolo, M Schwarz, On the Floer homology of cotangent bundles, Comm. Pure Appl. Math. 59 (2006) 254 MR2190223
2 A Abbondandolo, M Schwarz, Floer homology of cotangent bundles and the loop product, Geom. Topol. 14 (2010) 1569 MR2679580
3 M A Batanin, Symmetrisation of $n$–operads and compactification of real configuration spaces, Adv. Math. 211 (2007) 684 MR2323542
4 C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
5 R Bott, C Taubes, On the self-linking of knots, J. Math. Phys. 35 (1994) 5247 MR1295465
6 M Chas, D Sullivan, String topology, to appear in Ann. of Math. arXiv:math/9911159
7 K Cieliebak, A Floer, H Hofer, Symplectic homology II: A general construction, Math. Z. 218 (1995) 103 MR1312580
8 R L Cohen, K Hess, A A Voronov, String topology and cyclic homology, Adv. Courses in Math. CRM Barcelona, Birkhäuser (2006) MR2251006
9 R L Cohen, J D S Jones, A homotopy theoretic realization of string topology, Math. Ann. 324 (2002) 773 MR1942249
10 K Costello, Topological conformal field theories and Calabi–Yau categories, Adv. Math. 210 (2007) 165 MR2298823
11 V A Dolgushev, D E Tamarkin, B L Tsygan, Proof of Swiss cheese version of Deligne's conjecture, Int. Math. Res. Not. 2011 (2011) 4666 MR2844935
12 G Drummond-Cole, B Vallette, The minimal model for the Batalin–Vilkovisky operad arXiv:1105.2008
13 Y Félix, L Menichi, J C Thomas, Gerstenhaber duality in Hochschild cohomology, J. Pure Appl. Algebra 199 (2005) 43 MR2134291
14 I Galvez-Carrillo, A Tonks, B Vallette, Homotopy Batalin–Vilkovisky algebras arXiv:0907.2246
15 M Gerstenhaber, The cohomology structure of an associative ring, Ann. of Math. 78 (1963) 267 MR0161898
16 E Getzler, Cartan homotopy formulas and the Gauss–Manin connection in cyclic homology, from: "Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992)" (editors A Joseph, S Shnider), Israel Math. Conf. Proc. 7, Bar-Ilan Univ. (1993) 65 MR1261901
17 E Getzler, Batalin–Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (1994) 265 MR1256989
18 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
19 J Giansiracusa, P Salvatore, Formality of the framed little $2$–discs operad and semidirect products, from: "Homotopy theory of function spaces and related topics" (editors Y Félix, G Lupton, S B Smith), Contemp. Math. 519, Amer. Math. Soc. (2010) 115 MR2648708
20 V Hinich, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997) 3291 MR1465117
21 T V Kadeishvili, The structure of the $A(\infty)$–algebra, and the Hochschild and Harrison cohomologies, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 91 (1988) 19 MR1029003
22 R M Kaufmann, On several varieties of cacti and their relations, Algebr. Geom. Topol. 5 (2005) 237 MR2135554
23 R M Kaufmann, Moduli space actions on the Hochschild co-chains of a Frobenius algebra I: Cell operads, J. Noncommut. Geom. 1 (2007) 333 MR2314100
24 R M Kaufmann, Moduli space actions on the Hochschild co-chains of a Frobenius algebra II: Correlators, J. Noncommut. Geom. 2 (2008) 283 MR2411420
25 R M Kaufmann, A proof of a cyclic version of Deligne's conjecture via cacti, Math. Res. Lett. 15 (2008) 901 MR2443991
26 R M Kaufmann, M Livernet, R C Penner, Arc operads and arc algebras, Geom. Topol. 7 (2003) 511 MR2026541
27 R M Kaufmann, R Schwell, Associahedra, cyclohedra and a topological solution to the $A_\infty$ Deligne conjecture, Adv. Math. 223 (2010) 2166 MR2601011
28 M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)" (editors A Joseph, F Mignot, F Murat, B Prum, R Rentschler), Progr. Math. 120, Birkhäuser (1994) 97 MR1341841
29 M Kontsevich, Y Soibelman, Deformations of algebras over operads and the Deligne conjecture, from: "Conférence Moshé Flato 1999, Vol. I (Dijon)", Math. Phys. Stud. 21, Kluwer Acad. Publ. (2000) 255 MR1805894
30 K Lefevre-Hasegama, Sur les $a_\infty$ categories arXiv:abs/0310337
31 J L Loday, Cyclic homology, Grundl. Math. Wissen. 301, Springer (1998) MR1600246
32 J L Loday, B Vallette, Algebraic operads version0.99, book preprint (2011) arXiv:http://math.unice.fr/ brunov/Operades.html
33 M Markl, S Shnider, J Stasheff, Operads in algebra, topology and physics, Math. Surveys and Monogr. 96, Amer. Math. Soc. (2002) MR1898414
34 J E McClure, J H Smith, A solution of Deligne's Hochschild cohomology conjecture, from: "Recent progress in homotopy theory (Baltimore, MD, 2000)" (editor D M Davis), Contemp. Math. 293, Amer. Math. Soc. (2002) 153 MR1890736
35 L Menichi, Batalin–Vilkovisky algebras and cyclic cohomology of Hopf algebras, $K$–Theory 32 (2004) 231 MR2114167
36 P Seidel, Fukaya categories and deformations, from: "Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002)" (editor T Li), Higher Ed. Press (2002) 351 MR1957046
37 P Seidel, Fukaya categories and Picard–Lefschetz theory, Zurich Lectures in Adv. Math., European Math. Soc. (2008) MR2441780
38 P Seidel, Symplectic homology as Hochschild homology, from: "Algebraic geometry—Seattle 2005. Part 1" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math., Amer. Math. Soc. (2009) 415 MR2483942
39 P Ševera, Formality of the chain operad of framed little disks, Lett. Math. Phys. 93 (2010) 29 MR2661521
40 D Tamarkin, B Tsygan, Noncommutative differential calculus, homotopy BV algebras and formality conjectures, Methods Funct. Anal. Topology 6 (2000) 85 MR1783778
41 T Tradler, The Batalin–Vilkovisky algebra on Hochschild cohomology induced by infinity inner products, Ann. Inst. Fourier (Grenoble) 58 (2008) 2351 MR2498354
42 T Tradler, M Zeinalian, On the cyclic Deligne conjecture, J. Pure Appl. Algebra 204 (2006) 280 MR2184812
43 C Viterbo, Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999) 985 MR1726235
44 A A Voronov, Homotopy Gerstenhaber algebras, from: "Conférence Moshé Flato 1999, Vol. II (Dijon)" (editors G Dito, D Sternheimer), Math. Phys. Stud. 22, Kluwer Acad. Publ. (2000) 307 MR1805923
45 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
46 N Wahl, C Westerland, Hochschild homology of structured algebras arXiv:1110.0651