Properties Of Hamiltonian Torus Actions On Closed Symplectic Manifolds PDF Download
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Author | : Andrew L. Fanoe |
Publisher | : |
Total Pages | : |
Release | : 2013 |
Genre | : |
ISBN | : |
Download Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds Book in PDF, ePub and Kindle
This lends support to the conjecture that there are no such actions with a non-empty set of isolated fixed points.
Author | : Michèle Audin |
Publisher | : Birkhäuser |
Total Pages | : 181 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034872216 |
Download The Topology of Torus Actions on Symplectic Manifolds Book in PDF, ePub and Kindle
The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.
Author | : Michèle Audin |
Publisher | : Birkhäuser |
Total Pages | : 331 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034879601 |
Download Torus Actions on Symplectic Manifolds Book in PDF, ePub and Kindle
The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.
Author | : Ana Cannas da Silva |
Publisher | : Springer |
Total Pages | : 240 |
Release | : 2004-10-27 |
Genre | : Mathematics |
ISBN | : 354045330X |
Download Lectures on Symplectic Geometry Book in PDF, ePub and Kindle
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 | : Milena Dorota Pabiniak |
Publisher | : |
Total Pages | : 124 |
Release | : 2012 |
Genre | : |
ISBN | : |
Download Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology Book in PDF, ePub and Kindle
The central theme of this work are Hamiltonian torus actions on symplectic manifolds. We investigate the invariants of the action, and use the action to answer questions about the invariants of the manifold itself.
Author | : Victor Guillemin |
Publisher | : American Mathematical Soc. |
Total Pages | : 92 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 9780821842362 |
Download Convexity Properties of Hamiltonian Group Actions Book in PDF, ePub and Kindle
This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the "generic" case, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations. It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel su This volume is recommended for independent study and is suitable for graduate students and researchers interested in symplectic geometry, algebraic geometry, and geometric combinatorics. Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.
Author | : V. M. Buchstaber |
Publisher | : American Mathematical Soc. |
Total Pages | : 154 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821831860 |
Download Torus Actions and Their Applications in Topology and Combinatorics Book in PDF, ePub and Kindle
Here, the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a propermanifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects include simplicial and cubical complexes, polytopes, and arrangements. This approachalso provides a natural topological interpretation in terms of torus actions of many constructions from commutative and homological algebra used in combinatorics. The exposition centers around the theory of moment-angle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and well-known open problems and would be suitable as a textbook. It will be useful for specialists both in topology and in combinatoricsand will help to establish even tighter connections between the subjects involved.
Author | : Michèle Audin |
Publisher | : Springer Verlag |
Total Pages | : 225 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9780817621674 |
Download Symplectic Geometry of Integrable Hamiltonian Systems Book in PDF, ePub and Kindle
Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. This book serves as an introduction to symplectic and contact geometry for graduate students, exploring the underlying geometry of integrable Hamiltonian systems. Includes exercises designed to complement the expositiont, and up-to-date references.
Author | : Augustin Banyaga |
Publisher | : World Scientific |
Total Pages | : 178 |
Release | : 2016-08-08 |
Genre | : Mathematics |
ISBN | : 9814696722 |
Download A Brief Introduction To Symplectic And Contact Manifolds Book in PDF, ePub and Kindle
The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter.We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry.The book contains also more advanced material, suitable to advanced graduate students and researchers.
Author | : Charles Benedict Thomas |
Publisher | : Cambridge University Press |
Total Pages | : 332 |
Release | : 1996-09-28 |
Genre | : Mathematics |
ISBN | : 9780521570862 |
Download Contact and Symplectic Geometry Book in PDF, ePub and Kindle
This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. The two parts each contain a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before, and the lectures on Floer homology is the first avaliable in book form.Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention.