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Author: Victor Guillemin Publisher: Birkhauser ISBN: 9783764337704 Category : Convex polytopes Languages : en Pages : 150
Book Description
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. This book is addressed to researchers and can be used as a semester text.
Author: Victor Guillemin Publisher: Springer Science & Business Media ISBN: 1461202698 Category : Mathematics Languages : en Pages : 158
Book Description
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. This book is addressed to researchers and can be used as a semester text.
Author: Victor Guillemin Publisher: Birkhauser ISBN: 9783764337704 Category : Convex polytopes Languages : en Pages : 150
Book Description
The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. This book is addressed to researchers and can be used as a semester text.
Author: Juan-Pablo Ortega Publisher: Springer Science & Business Media ISBN: 1475738110 Category : Mathematics Languages : en Pages : 526
Book Description
* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.
Author: H. Pedersen Publisher: CRC Press ISBN: 1000110850 Category : Mathematics Languages : en Pages : 766
Book Description
"Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."
Author: Selim Tawfik Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
A fusion product is defined for Hamiltonian spaces with moment maps valued in a Lie group D generalizing those of Alekseev-Malkin-Meinrenken. An analogous theory for these general Hamiltonian spaces is developed and, among other results, versions of symplectic reduction, duality and the shifting trick are derived. The Hamiltonian spaces with moment maps valued in a homogeneous space D/G of Alekseev-Kosmann-Schwarzbach are shown to be equivalent to certain Hamiltonian spaces with group-valued moment maps. The aforementioned theory is consequently brought to bear on that of D/G-valued moment maps, thereby defining a fusion product for these. This fusion product affords many new examples of D/G-valued moment maps, of which there was hitherto a paucity. Among said examples are moduli spaces of flat principal bundles over certain surfaces with boundary.
Author: Megumi Harada Publisher: American Mathematical Soc. ISBN: 0821844865 Category : Mathematics Languages : en Pages : 424
Book Description
Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the fieldare provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry.This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above. Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students andresearchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.
Author: Ana Cannas da Silva Publisher: Springer ISBN: 354045330X Category : Mathematics Languages : en Pages : 240
Book Description
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author: Johan Dubbeldam Publisher: John Wiley & Sons ISBN: 3527409319 Category : Science Languages : en Pages : 261
Book Description
Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.
Author: Victor Guillemin
Author: Victor Guillemin
Author: Victor Guillemin
Author: Juan-Pablo Ortega
Author: H. Pedersen
Author: Selim Tawfik
Author: Megumi Harada
Author: Ana Cannas da Silva
Author: Victor Guillemin
Author: Johan Dubbeldam
Author: Sylvain Cappell