Algebraic & Geometric Topology Volume 10, issue 3 (2010)

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

On the Rozansky–Witten weight systems

Justin Roberts and Simon Willerton

Algebraic & Geometric Topology 10 (2010) 1455–1519

DOI: 10.2140/agt.2010.10.1455

Bibliography

1	M F Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957) 181 MR0086359
2	B Bakalov, A Kirillov Jr., Lectures on tensor categories and modular functors, 21, Amer. Math. Soc. (2001) MR1797619
3	D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
4	D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, Wheels, wheeling, and the Kontsevich integral of the unknot, Israel J. Math. 119 (2000) 217 MR1802655
5	D Bar-Natan, T T Q Le, D P Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geom. Topol. 7 (2003) 1 MR1988280
6	A Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983) MR730926
7	N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, 298, Springer (1992) MR1215720
8	A Căldăraru, The Mukai pairing. II. The Hochschild–Kostant–Rosenberg isomorphism, Adv. Math. 194 (2005) 34 MR2141853
9	V Chari, A Pressley, A guide to quantum groups, Cambridge Univ. Press (1994) MR1300632
10	P Deligne, J W Morgan, Notes on supersymmetry (following Joseph Bernstein), from: "Quantum fields and strings : a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997)" (editors P Deligne, P Etingof, D S Freed, L C Jeffrey, D Kazhdan, J W Morgan, D R Morrison, E Witten), Amer. Math. Soc. (1999) 41 MR1701597
11	V G Drinfel′d, Quasi-Hopf algebras, Algebra i Analiz 1 (1989) 114 MR1047964
12	M Duflo, Caractères des groupes et des algèbres de Lie résolubles, Ann. Sci. École Norm. Sup. (4) 3 (1970) 23 MR0269777
13	S I Gelfand, Y I Manin, Homological algebra, Springer (1999) MR1698374
14	M Gerstenhaber, S D Schack, Algebras, bialgebras, quantum groups, and algebraic deformations, from: "Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990)" (editors M Gerstenhaber, J Stasheff), Contemp. Math. 134, Amer. Math. Soc. (1992) 51 MR1187279
15	D Guan, Examples of compact holomorphic symplectic manifolds which are not Kählerian. II, Invent. Math. 121 (1995) 135 MR1345287
16	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
17	V Hinich, A Vaintrob, Cyclic operads and algebra of chord diagrams, Selecta Math. (N.S.) 8 (2002) 237 MR1913297
18	N Hitchin, Hyper-Kähler manifolds, from: "Séminaire Bourbaki, Vol. 1991/92", Astérisque 206, Soc. Math. France (1992) 3, 137 MR1206066
19	N Hitchin, J Sawon, Curvature and characteristic numbers of hyper-Kähler manifolds, Duke Math. J. 106 (2001) 599 MR1813238
20	M Kapranov, Rozansky–Witten invariants via Atiyah classes, Compositio Math. 115 (1999) 71 MR1671737
21	M Kashiwara, P Schapira, Sheaves on manifolds, 292, Springer (1994) MR1299726
22	C Kassel, Quantum groups, 155, Springer (1995) MR1321145
23	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
24	M Kontsevich, Rozansky–Witten invariants via formal geometry, Compositio Math. 115 (1999) 115 MR1671725
25	M Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003) 157 MR2062626
26	T T Q Le, J Murakami, Parallel version of the universal Vassiliev-Kontsevich invariant, J. Pure Appl. Algebra 121 (1997) 271 MR1477611
27	T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of 3–manifolds, Topology 37 (1998) 539 MR1604883
28	N Markarian, Poincaré–Birkhoff–Witt isomorphism and Riemann–Roch, Preprint (2000)
29	J Murakami, T Ohtsuki, Topological quantum field theory for the universal quantum invariant, Comm. Math. Phys. 188 (1997) 501 MR1473309
30	M Nieper-Wißkirchen, Chern numbers and Rozansky–Witten invariants of compact hyper-Kähler manifolds, World Scientific (2004) MR2110899
31	K G O’Grady, Desingularized moduli spaces of sheaves on a K3, J. Reine Angew. Math. 512 (1999) 49 MR1703077
32	K G O’Grady, A new six-dimensional irreducible symplectic variety, J. Algebraic Geom. 12 (2003) 435 MR1966024
33	A C Ramadoss, The big Chern classes and the Chern character, Internat. J. Math. 19 (2008) 699 MR2431634
34	J Roberts, Rozansky–Witten theory, from: "Topology and geometry of manifolds (Athens, GA, 2001)" (editors G Matić, C McCrory), Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 1 MR2024627
35	J Roberts, J Sawon, Generalisations of Rozansky–Witten invariants, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)" (editors T Ohtsuki, T Kohno, T Le, J Murakami, J Roberts, V Turaev), Geom. Topol. Monogr. 4, Geom. Topol. Publ. (2002) 263 MR2002615
36	L Rozansky, E Witten, Hyper-Kähler geometry and invariants of three-manifolds, Selecta Math. (N.S.) 3 (1997) 401 MR1481135
37	J Sawon, Rozansky–Witten invariants of hyperkähler manifolds, PhD thesis, University of Cambridge (1999)
38	R P Thomas, Derived categories for the working mathematician, from: "Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999)" (editors C Vafa, S T Yau), AMS/IP Stud. Adv. Math. 23, Amer. Math. Soc. (2001) 349 MR1876077
39	V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673
40	A Vaintrob, Vassiliev knot invariants and Lie S–algebras, Math. Res. Lett. 1 (1994) 579 MR1295552
41	P Vogel, Algebraic structures on modules of diagrams, Preprint (1995)