Prof. dr. M.N. (Marius) Crainic
Professor
Publications
2020
Scholarly publications
Cattafi, F., Crainic, M. N., & Salazar Pinzon, M. A. (2020). From PDEs to Pfaffian fibrations. Journal of the European Mathematical Society, 66(1/2), 187-250. https://doi.org/10.4171/LEM/66-1/2-10
2018
Scholarly publications
Crainic, M., & Mestre, J. N. (2018). Orbispaces as differentiable stratified spaces. Letters in Mathematical Physics, 108(3), 805-859. https://doi.org/10.1007/s11005-017-1011-6
2015
Scholarly publications
Crainic, M., & Marcut, I. (2015). Reeb-Thurston stability for symplectic foliations. Mathematische Annalen, 363, 217–235. https://doi.org/10.1007/s00208-014-1167-7
2014
Scholarly publications
Crainic, M., Schätz, F., & Struchiner, I. (2014). A survey on stability and rigidity results for Lie algebras. Indagationes Mathematicae, 25(5), 957–976. https://doi.org/10.1016/j.indag.2014.07.015
Crainic, M., Salazar Pinzon, M., & Struchiner, I. (2014). Multiplicative forms and Spencer operators. Mathematische Zeitschrift. https://doi.org/10.1007/s00209-014-1398-z
2013
Scholarly publications
Crainic, M. N., & Struchiner, I. (2013). On the linearization theorem for proper Lie groupoids. Annales scientifiques de l'Ecole Normale Supérieure, 46(5), 723-746.
Crainic, M. N., & Abad, A. (2013). Representations up to homotopy and Bott's spectral sequence for Lie groupoids. Advances in Mathematics, 248, 416-452. https://doi.org/10.1016/j.aim.2012.12.022
2012
Scholarly publications
Crainic, M. N., & Marcut, I. T. (2012). A normal form theorem around symplectic leaves. Journal of Differential Geometry, 92(3), 417-461. https://doi.org/10.4310/jdg/1354110196
2011
Scholarly publications
Arias Abad, C., & Crainic, M. (2011). Representations up to homotopy of Lie algebroids. Journal fur die Reine und Angewandte Mathematik, 663, 91-126. https://doi.org/10.1515/CRELLE.2011.095
Crainic, M., & Fernandes, R. L. (2011). Lectures on integrability of Lie brackets. In T. Ratiu, A. Weinstein, & N. T. Zung (Eds.), Lectures on Poisson Geometry (pp. 1-107). (Geometry & topology monographs; No. 117). Mathematical Sciences Publishers.
Crainic, M. (2011). Generalized complex structures and Lie brackets. Bulletin of the Brazilian Mathematical Society, 42(4), 559-578. https://doi.org/10.1007/s00574-011-0029-0
Arias Abad, C., Crainic, M., & Dherin, B. R. U. (2011). Tensor products of representations up to homotopy. Journal of Homotopy and Related Structures, 6(2), 239-288.
Crainic, M., & Marcut, I. T. (2011). On the existence of symplectic realizations. Journal of Symplectic Geometry, 9(4), 435-444.
Arias Abad, C., & Crainic, M. (2011). The Weil algebra and the Van Est isomorphism. Annales de l'Institut Fourier, 61(3), 927-970. https://doi.org/10.5802/aif.2633
Crainic, M., & Fernandes, R. L. (2011). A geometric approach to Conn's linearization theorem. Annals of Mathematics, 173, 1121-1139. https://doi.org/10.4007/annals.2011.173.2.14
2010
Scholarly publications
Crainic, M., & Crainic, N. (2010). Polya conditions for multivariate Birkhoff interpolation: from general to rectangular sets of nodes. Acta Mathematica Universitatis Comenianae, 79(1), 9-18.
https://dspace.library.uu.nl/bitstream/handle/1874/203046/crainic.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/203046/crainic.pdf?sequence=1
Crainic, M., & Fernandes, R. L. (2010). Stability of symplectic leaves. Inventiones Mathematicae, 180, 481-533. https://doi.org/10.1007/s00222-010-0235-1
2009
Scholarly publications
Crainic, M., & Crainic, N. (2009). Normal bivariate Birkhoff interpolation schemes and Pell equation. Commentationes Mathematicae Universitatis Carolinae, 50(2), 265-272.
Bursztyn, H., & Crainic, M. (2009). Dirac geometry, quasi-Poisson actions and D/G-valued moment maps. Journal of Differential Geometry, 82(3), 501-566.
2008
Scholarly publications
Moerdijk, I., & Crainic, M. (2008). Deformations of Lie brackets: cohomological aspects. Journal of the European Mathematical Society, 10, 1037-1059.
Crainic, M., & Crainic, N. (2008). Brikhoff interpolation with rectangular sets of nodes and with few derivatives. East Journal on Approximations, 14(4), 423-437.
2007
Scholarly publications
Crainic, M., & Zhu, C. (2007). Integrability of Jacobi and Poisson structures. Annales de l'Institut Fourier, 57(4), 1181-1216.
2005
Scholarly publications
Bursztyn, H., & Crainic, M. (2005). Dirac structures, momentum maps, and quasi-Poisson manifolds. In The breadth of symplectic and Poisson geometry (pp. 1-40). Birkhaüser.
Crainic, M., & Fernandes, R. L. (2005). Secondary characteristic classes of Lie algebroids. In Quantum field theory and noncommutative geometry (Vol. 662, pp. 157-176). Springer. http://link.springer.com/chapter/10.1007%2F11342786_9
2004
Scholarly publications
Crainic, M., & Fernandes, R. L. (2004). Integrability of Poisson brackets. Journal of Differential Geometry, 66, 71-137.
Moerdijk, I., & Crainic, M. (2004). Cech-De Rham theory for leaf spaces of foliations. Mathematische Annalen, 328, 59-85.
Bursztyn, H., Crainic, M., Weinstein, R. A., & Zhu, C. (2004). Integration of twisted Dirac brackets. Duke Mathematical Journal, 123, 549-607.
2003
Scholarly publications
Fernandes, R. L., & Crainic, M. (2003). Loja Integrability of Lie brackets. Annals of Mathematics, 157(2), 575-620.
Crainic, M. (2003). Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes. Commentarii Mathematici Helvetici, 78, 681-721.
2002
Scholarly publications
Crainic, M. (2002). Cyclic cohomology of Hopf algebras. Journal of Pure and Applied Algebra, 166(1-2), 29-66.
2001
Scholarly publications
Crainic, M., & Moerdijk, I. (2001). Foliation groupoids and their cyclic homology. Advances in Mathematics, 157(2), 177-197.
2000
Scholarly publications
Moerdijk, I., & Crainic, M. (2000). A homology theory for étale groupoids. Journal fur die Reine und Angewandte Mathematik, 521, 25-46.
Crainic, M. (2000). Cyclic cohomology and characteristic classes for foliations. [Doctoral thesis 1 (Research UU / Graduation UU), Universiteit Utrecht].
1999
Scholarly publications
Ostvoor, P., & Crainic, M. (1999). On two-primary algebraic K-theory of quadratic number rings with focus on K/2. Acta Arithmetica, 87, 223-243.
Crainic, M. (1999). Cyclic cohomology of étale groupoids; The general case. K-Theory, 17(4), 319-362.
1997
Scholarly publications
Varga, C., & Crainic, M. (1997). A note on the denseness of complete invariant metrics. Publicationes Mathematicae, 51.