Algebraic & Geometric Topology Volume 14, issue 1 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Koszul duality theory for operads over Hopf algebras

Olivia Bellier

Algebraic & Geometric Topology 14 (2014) 1–35

DOI: 10.2140/agt.2014.14.1

Bibliography

1	S Barannikov, M Kontsevich, Frobenius manifolds and formality of Lie algebras of polyvector fields, Internat. Math. Res. Notices (1998) 201 MR1609624
2	I A Batalin, G A Vilkovisky, Gauge algebra and quantization, from: "Quantum gravity" (editors M A Markov, P C West), Plenum (1984) 463 MR746994
3	C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
4	H D Cao, J Zhou, DGBV algebras and mirror symmetry, from: "First International Congress of Chinese Mathematicians" (editors L Yang, S T Yau), AMS/IP Stud. Adv. Math. 20, Amer. Math. Soc. (2001) 279 MR1830184
5	H D Cao, J Zhou, On quasi-isomorphic DGBV algebras, Math. Ann. 326 (2003) 459 MR1992272
6	M Chas, D Sullivan, String topology arXiv:9911159
7	P Deligne, P Griffiths, J Morgan, D Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975) 245 MR0382702
8	G C Drummond-Cole, Formal formality of the hypercommutative algebras of low dimensional Calabi–Yau varieties arXiv:1201.6111
9	G C Drummond-Cole, B Vallette, The minimal model for the Batalin–Vilkovisky operad, Selecta Math. 19 (2013) 1 MR3029946
10	I Gálvez-Carrillo, A Tonks, B Vallette, Homotopy Batalin–Vilkovisky algebras, J. Noncommut. Geom. 6 (2012) 539 MR2956319
11	E Getzler, Batalin–Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (1994) 265 MR1256989
12	E Getzler, Two-dimensional topological gravity and equivariant cohomology, Comm. Math. Phys. 163 (1994) 473 MR1284793
13	E Getzler, J D S Jones, Operads, homotopy algebra and iterated integrals for double loop spaces arXiv:9403055
14	V Ginzburg, M Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203 MR1301191
15	E Hoffbeck, A Poincaré–Birkhoff–Witt criterion for Koszul operads, Manuscripta Math. 131 (2010) 87 MR2574993
16	T V Kadeishvili, The algebraic structure in the homology of an A(∞)–algebra, Soobshch. Akad. Nauk Gruzin. SSR 108 (1982) 249 MR720689
17	M Kontsevich, Homological algebra of mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2" (editor S D Chatterji), Birkhäuser (1995) 120 MR1403918
18	P Van der Laan, Coloured Koszul duality and strongly homotopy operads arXiv:0312147
19	B H Lian, G J Zuckerman, New perspectives on the BRST-algebraic structure of string theory, Comm. Math. Phys. 154 (1993) 613 MR1224094
20	M Livernet, C Roitzheim, S Whitehouse, Derived A_∞–algebras in an operadic context, Algebr. Geom. Topol. 13 (2013) 409 MR3031646
21	J L Loday, B Vallette, Algebraic operads, 346, Springer (2012) MR2954392
22	Y I Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, 47, Amer. Math. Soc. (1999) MR1702284
23	M Markl, Distributive laws and Koszulness, Ann. Inst. Fourier (Grenoble) 46 (1996) 307 MR1393517
24	P Salvatore, N Wahl, Framed discs operads and Batalin–Vilkovisky algebras, Q. J. Math. 54 (2003) 213 MR1989873
25	J D Stasheff, Homotopy associativity of H–spaces : I, II, Trans. Amer. Math. Soc. 108, 275-292; ibid. 108 (1963) 293 MR0158400
26	M E Sweedler, Hopf algebras, , W. A. Benjamin (1969) MR0252485
27	B Vallette, Homotopy theory of homotopy algebras (2013)