Integration of exact Courant algebroids
Pages: 58  76,
January
2012
doi:10.3934/era.2012.19.58 Abstract
References
Full text (431.5K)
Related Articles
David LiBland  Department of Mathematics, University of Toronto, 40 St George Street, Toronto, Ontario M4S2E4, Canada (email)
Pavol Ševera  Department of Mathematics, Université de Genève, Geneva, Switzerland (email)
1 
C. Arias Abad and M. Crainic, Representations up to homotopy of Lie algebroids, 2009. Available from: http://arxiv.org/pdf/0901.0319v2. 

2 
C. Arias Abad and F. Schaetz, The $A_\infty$ de Rham theorem and integration of representations up to homotopy, 2010. Available from: http://arxiv.org/pdf/1011.4693. 

3 
M. Artin and B. Mazur, On the van Kampen theorem, Topology, 5 (1966), 179189. 

4 
C. Blohmann, M. C. B. Fernandes and A. Weinstein, Groupoid symmetry and constraints in general relativity, March, 2010. Available from: http://arxiv.org/pdf/1003.2857v2. 

5 
H. Bursztyn and A. Cabrera, Multiplicative forms at the infinitesimal level, (2010), 135. Available from: http://arxiv.org/pdf/1001.0534v2. 

6 
H. Bursztyn, A. Cabrera and C. Ortiz, Linear and multiplicative 2forms, Letters in Mathematical Physics, 90 (2009), 5983. 

7 
H. Bursztyn, M. Crainic, A. Weinstein and C. Zhu, Integration of twisted Dirac brackets, Duke Mathematical Journal, 123 (2004), 549607. 

8 
A. S. Cattaneo, Integration of twisted Poisson structures, Journal of Geometry and Physics, 49 (2004), 187196. 

9 
A. S. Cattaneo, B. Dherin and A. Weinstein, Symplectic microgeometry I: Micromorphisms, The Journal of Symplectic Geometry, 8 (2010), 205223. 

10 
A. M. Cegarra and J. Remedios, The relationship between the diagonal and the bar constructions on a bisimplicial set, Topology and its Applications, 153 (2005), 2151. 

11 
M. Crainic, Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes, Commentarii Mathematici Helvetici, 78 (2003), 681721. 

12 
M. Crainic and R. L. Fernandes, Integrability of Lie brackets, Annals of Mathematics (2), 157 (2003), 575620. 

13 
M. Crainic and R. L. Fernandes, Integrability of Poisson brackets, Journal of Differential Geometry, 66 (2004), 71137. 

14 
P. G. Goerss and J. F. Jardine, "Simplicial Homotopy Theory," Reprint of the 1999 edition, Modern Birkhäuser Classics, Birkhäuser Verlag, Basel, 2009. 

15 
A. GraciaSaz and R. A. Mehta, Lie algebroid structures on double vector bundles and representation theory of Lie algebroids, Advances in Mathematics, 223 (2010), 12361275. 

16 
A. GraciaSaz and R. A. Mehta, VBgroupoids and representation theory of Lie groupoids, (2011), 131. Available from: http://arxiv.org/pdf/1007.3658. 

17 
A. Henriques, Integrating $L_\infty$algebras, Compositio Mathematica, 144 (2008), 10171045. 

18 
D. Iglesias Ponte, C. LaurentGengoux and P. Xu, Universal lifting theorem and quasiPoisson groupoids, (2005), 146. Available from: http://arxiv.org/pdf/math/0507396v1. 

19 
D. Kochan, Differential gorms and worms, in "Mathematical Physics," 128130. World Sci. Publ., Hackensack, NJ, 2005. 

20 
M. Kontsevich, Deformation quantization of Poisson manifolds, Letters in Mathematical Physics, 66 (2003), 157216. 

21 
Y. KosmannSchwarzbach, Quasi, twisted, and all that$\ldots$in Poisson geometry and Lie algebroid theory, in "The Breadth of Symplectic and Poisson Geometry, Birkhäuser Boston, Boston, MA, (2005), 363389. 

22 
K. C. H. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Mathematical Journal, 73 (1994), 415452. 

23 
K. C. H. Mackenzie and P. Xu, Integration of Lie bialgebroids, Topology, 39 (2000), 445467. 

24 
R. A. Mehta and X. Tang, From double Lie groupoids to local Lie 2groupoids, Bulletin of the Brazilian Mathematical Society (New Series), 42 (2011), 651681. Available from: http://arxiv.org/pdf/1012.4103. 

25 
J. W. Milnor, Microbundles. I, Topology, 3 (1964), 5380. 

26 
D. Roytenberg, "Courant Algebroids, Derived Brackets and Even Symplectic Supermanifolds," Ph.D. thesis, University of California, Berkeley, 1999. 

27 
D. Roytenberg, On the structure of graded symplectic supermanifolds and Courant algebroids, in "Quantization, Poisson Brackets and Beyond" (Manchester, 2001), Contemp. Math., 315, Amer. Math. Soc., Providence, RI, (2002), 169185. 

28 
D. Roytenberg, QuasiLie bialgebroids and twisted Poisson manifolds, Letters in Mathematical Physics, 61 (2002), 123137. 

29 
D. Roytenberg and A. Weinstein, Courant algebroids and strongly homotopy Lie algebras, Letters in Mathematical Physics, 46 (1998), 8193. 

30 
P. Ševera, "Letters to A. Weinstein." Available from: http://sophia.dtp.fmph.uniba.sk/~severa/letters/. 

31 
P. Ševera, Some title containing the words "homotopy" and "symplectic", e.g. this one, in "Travaux Mathématiques. Fasc. XVI," Univ. Luxemb., Luxembourg, (2005), 121137. 

32 
P. Ševera, $L_\infty$algebras as first approximations, in "XXVI Workshop on Geometrical Methods in Physics," AIP Conf. Proc., 956, Amer. Inst. of Physics, Melville, NY, (2007), 199204. 

33 
P. Ševera and A. Weinstein, Poisson geometry with a 3form background, Progress of Theoretical Physics Suppl., 144 (2001), 145154. 

34 
Y. Sheng and C. Zhu, Higher extensions of lie algebroids and application to courant algebroids, 2011. Available from: http://arxiv.org/pdf/1103.5920. 

35 
Y. Sheng and C. Zhu, Semidirect products of representations up to homotopy, Pacific Journal of Mathematics, 249 (2011), 211236. 

36 
P. Xu, On Poisson groupoids, International Journal of Mathematics, 6 (1995), 101124. 

37 
C. Zhu, Kan replacement of simplicial manifolds, Letters in Mathematical Physics, 90 (2009), 383405. 

Go to top
