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Almost-bieberbach groups : affine and polynomial structures par Dekimpe, Karel. Publication : [S.l.] Springer 2009 . 262 p. , Starting from basic knowledge of nilpotent (Lie) groups, an algebraic theory of almost-Bieberbach groups, the fundamental groups of infra-nilmanifolds, is developed. These are a natural generalization of the well known Bieberbach groups and many results about ordinary Bieberbach groups turn out to generalize to the almost-Bieberbach groups. Moreover, using affine representations, explicit cohomology computations can be carried out, or resulting in a classification of the almost-Bieberbach groups in low dimensions. The concept of a polynomial structure, an alternative for the affine structures that sometimes fail, is introduced. 24 cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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An Introduction to geometrical physics / par Aldrovandi, R. Publication : [S.l.] : World Scientific Publishing Company, 1995 . 699 p. ; , This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and others subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation. The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level of understanding, a more advanced treatment of the mathematical topics. It is aimed as an elementary text, more so than most others on the market, and is intended for first year graduate students. 22 cm. Date : 1995 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Complex geometry : an introduction / par Huybrechts, Daniel. Publication : Berlin ; | New York : Springer, 2005 . xii, 309 p. : 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Introduction to symplectic dirac operators / par Habermann, Katharina. Publication : [S.l.] : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2006 . 124 p. ; , BrochØ. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Noncommutative geometry, quantum fields and motives par Connes, Alain Publication : [S.l.] American Mathematical Society 2008 . 785 p. , The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adele class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function. 27 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Pfaffian systems, K-symplectic systems / par Awane, A. Publication : [S.l.] : Springer, 2000 . 260 p. ; , The geometrical view of mechanics is based on the study of certain exterior systems, the most classical of which are Pfaffian systems. In this book, we present the classification theorems (Frobenius, Darboux) and the local classification of Pfaffian systems of five variables, following Cartan. We also present a new class of exterior systems, called k-symplectic systems, generalizing the notion of symplectic form. These systems permit us to write in the language of exterior forms the equations proposed by Nambu for a model of statistical mechanics. Audience: This book is aimed at graduate students and at research workers in the field of mathematics, differential geometry, statistical mechanics, mathematics of physics and Lie algebras. 25 cm. Date : 2000 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Supermanifolds and supergroups basic theory par Tuynman, G. M. Publication : Dordrecht | Boston Kluwer Academic Publishers. 2004 . xiii, 416 pages 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Topology ii / par Fuchs, D. B. Publication : [S.l.] : Springer, 2004 . 295 p. ; , Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics. 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Initiation to global Finslerian geometry / par Akbar-Zadeh, H. Publication : . 1 online resource (xiii, 250 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780444521064,  http://www.sciencedirect.com/science/publication?issn=09246509&volume=68,

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Morse Theory and Floer Homology par Audin, Michèle. Publication : . XIV, 596 p. 114 illus. Disponibilité :  http://dx.doi.org/10.1007/978-1-4471-5496-9,

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The Implicit Function Theorem History, Theory, and Applications / par Krantz, Steven G. Publication : . XIII, 163 p. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-5981-1,

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First Steps in Differential Geometry Riemannian, Contact, Symplectic / par McInerney, Andrew. Publication : . XIII, 410 p. 54 illus., 25 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-7732-7,

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Introduction to Tensor Analysis and the Calculus of Moving Surfaces par Grinfeld, Pavel. Publication : . XIII, 302 p. 37 illus., 4 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-7867-6,

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Geometric Analysis of the Bergman Kernel and Metric par Krantz, Steven G. Publication : . XIII, 292 p. 7 illus. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-7924-6,

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Hermitian Analysis From Fourier Series to Cauchy-Riemann Geometry / par D'Angelo, John P. Publication : . X, 203 p. 27 illus., 19 illus. in color. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-8526-1,

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Geodesic Convexity in Graphs par Pelayo, Ignacio M. Publication : . VIII, 112 p. 41 illus. Disponibilité :  http://dx.doi.org/10.1007/978-1-4614-8699-2,

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