Moment Maps And Combinatorial Invariants Of Hamiltonian Tn Spaces
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Moment Maps And Combinatorial Invariants Of Hamiltonian Tn Spaces
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Author : Victor Guillemin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Moment Maps And Combinatorial Invariants Of Hamiltonian Tn Spaces written by Victor Guillemin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Moment Maps And Combinatorial Invariants Of Hamiltonian Tn Spaces
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Author : Victor Guillemin
language : en
Publisher: Birkhauser
Release Date : 1994
Moment Maps And Combinatorial Invariants Of Hamiltonian Tn Spaces written by Victor Guillemin and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Convex polytopes categories.
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.
Geometry And Physics
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Author : H. Pedersen
language : en
Publisher: CRC Press
Release Date : 2021-01-07
Geometry And Physics written by H. Pedersen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-07 with Mathematics categories.
"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."
Moment Maps Cobordisms And Hamiltonian Group Actions
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Author : Victor Guillemin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Moment Maps Cobordisms And Hamiltonian Group Actions written by Victor Guillemin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
Symplectic Actions Of 2 Tori On 4 Manifolds
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Author : Alvaro Pelayo
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-02-22
Symplectic Actions Of 2 Tori On 4 Manifolds written by Alvaro Pelayo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-22 with Mathematics categories.
In this paper the author classifies symplectic actions of $2$-tori on compact connected symplectic $4$-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. The author constructs explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants.
Toric Topology
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Author : Megumi Harada
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Toric Topology written by Megumi Harada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Toric Topology
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Author : Victor M. Buchstaber
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-07-15
Toric Topology written by Victor M. Buchstaber and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Algebraic topology categories.
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.
The Complexity Of Dynamical Systems
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Author : Johan Dubbeldam
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-21
The Complexity Of Dynamical Systems written by Johan Dubbeldam and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-21 with Science categories.
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.
Surveys On Surgery Theory Papers Dedicated To C T C Wall
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Author : Sylvain Cappell
language : en
Publisher: Princeton University Press
Release Date : 2000
Surveys On Surgery Theory Papers Dedicated To C T C Wall written by Sylvain Cappell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Handbook Of Differential Geometry
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Author : Franki J.E. Dillen
language : en
Publisher: Elsevier
Release Date : 2005-11-29
Handbook Of Differential Geometry written by Franki J.E. Dillen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-29 with Mathematics categories.
In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics