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                                                    3. Introduction to Foliations and Lie Groupoids
                                                    • Cited by 201
                                                    • Cited by
                                                      Crossref Citations
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                                                      This Book has been cited by the following publications. This list is generated based on data provided by Crossref.
                                                      Strobl, Thomas 2004. Algebroid Yang-Mills Theories. Physical Review Letters, Vol. 93, Issue. 21,
                                                      Ortega, Juan-Pablo and Ratiu, Judor S. 2004. Symmetry Reduction in Symplectic and Poisson Geometry. Letters in Mathematical Physics, Vol. 69, Issue. 1-3, p. 11.
                                                      Zambon, Marco and Zhu, Chenchang 2005. Contact reduction and groupoid actions. Transactions of the American Mathematical Society, Vol. 358, Issue. 3, p. 1365.
                                                      Oh, Yong-Geun and Park, Jae-Suk 2005. Deformations of coisotropic submanifolds and strong homotopy Lie algebroids. Inventiones mathematicae, Vol. 161, Issue. 2, p. 287.
                                                      WALDMANN, STEFAN 2006. THE COVARIANT PICARD GROUPOID IN DIFFERENTIAL GEOMETRY. International Journal of Geometric Methods in Modern Physics, Vol. 03, Issue. 03, p. 641.
                                                      BOS, ROGIER 2007. GEOMETRIC QUANTIZATION OF HAMILTONIAN ACTIONS OF LIE ALGEBROIDS AND LIE GROUPOIDS. International Journal of Geometric Methods in Modern Physics, Vol. 04, Issue. 03, p. 389.
                                                      MARCELINO, SÉRGIO and RESENDE, PEDRO 2008. An algebraic generalization of Kripke structures. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 145, Issue. 3, p. 549.
                                                      Kosmann-Schwarzbach, Y. Laurent-Gengoux, C. and Weinstein, A. 2008. Modular Classes of Lie Algebroid Morphisms. Transformation Groups, Vol. 13, Issue. 3-4, p. 727.
                                                      RENNIE, ADAM and VÁRILLY, JOSEPH C. 2008. ORBIFOLDS ARE NOT COMMUTATIVE GEOMETRIES. Journal of the Australian Mathematical Society, Vol. 84, Issue. 1, p. 109.
                                                      Lorenz, Arne 2008. On Local Integrability Conditions of Jet Groupoids. Acta Applicandae Mathematicae, Vol. 101, Issue. 1-3, p. 205.
                                                      Hofer, Helmut Wysocki, Kris and Zehnder, Eduard 2009. A general Fredholm theory III: Fredholm functors and polyfolds. Geometry & Topology, Vol. 13, Issue. 4, p. 2279.
                                                      Carrillo-Rouse, Paulo and Monthubert, Bertrand 2009. An index theorem for manifolds with boundary. Comptes Rendus. Mathématique, Vol. 347, Issue. 23-24, p. 1393.
                                                      Lerman, Eugene and Malkin, Anton 2009. Equivariant Differential Characters and Symplectic Reduction. Communications in Mathematical Physics, Vol. 289, Issue. 2, p. 777.
                                                      Hořava, Petr 2009. Membranes at quantum criticality. Journal of High Energy Physics, Vol. 2009, Issue. 03, p. 020.
                                                      Calcagni, Gianluca 2009. Cosmology of the Lifshitz universe. Journal of High Energy Physics, Vol. 2009, Issue. 09, p. 112.
                                                      Huebschmann, Johannes 2009. Equivariant Cohomology over Lie Groupoids and Lie–Rinehart Algebras. Letters in Mathematical Physics, Vol. 90, Issue. 1-3,
                                                      Hořava, Petr 2009. Quantum gravity at a Lifshitz point. Physical Review D, Vol. 79, Issue. 8,
                                                      Capasso, Dario and Polychronakos, Alexios P. 2010. General static spherically symmetric solutions in Hořava gravity. Physical Review D, Vol. 81, Issue. 8,
                                                      Nozawa, Hiraku 2010. Rigidity of the Álvarez class. manuscripta mathematica, Vol. 132, Issue. 1-2, p. 257.
                                                      Nozawa, Hiraku 2010. Minimizability of developable Riemannian foliations. Annals of Global Analysis and Geometry, Vol. 38, Issue. 2, p. 119.
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                                                    Publisher:
                                                    Cambridge University Press
                                                    Online publication date:
                                                    February 2010
                                                    Print publication year:
                                                    2003
                                                    Online ISBN:
                                                    9780511615450
                                                    DOI:
                                                    https://doi.org/10.1017/CBO9780511615450
                                                    Subjects:
                                                    Mathematics (general), Mathematics, Geometry and Topology, Algebra
                                                    Series:
                                                    Cambridge Studies in Advanced Mathematics (91)
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                                                    Book description

                                                    This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

                                                    Reviews

                                                    'The book is based on course lecture notes and it still keeps its qualities and nice presentation.'

                                                    Source: EMS Newsletter

                                                    'The book by Moerdijk and Mrcun serves as a concise and user-friendly introduction to the foundations of foliation theory and Lie groupoids, delving into just about all of the above-mentioned facets of the subject, and more. … the book reflects a great deal of care and thought on the part of the authors. … there is no apparent neglect of essential details, and the clarity of exposition is maintained right to the end. Those interested in the subject should find the book a delight to work through, and should thereby find a pathway into the more specialized topics mentioned earlier. … the treatment of each topic is as admirably self-contained as one might hope for. The instructional value of the book seems quite high, and it could certainly be recommended as text on which to base a graduate course.'

                                                    Source: Bulletin London Math Society

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