The Topology Of Torus Actions On Symplectic Manifolds

Author : Michèle Audin
Publisher : Birkhäuser
Page : 181 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034872218

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The Topology of Torus Actions on Symplectic Manifolds by Michèle Audin Pdf

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
Page : 331 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879606

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Torus Actions on Symplectic Manifolds by Michèle Audin Pdf

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 : Goutam Mukherjee
Publisher : Springer
Page : 140 pages
File Size : 46,6 Mb
Release : 2005-04-15
Category : Mathematics
ISBN : 9789386279309

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Transformation Groups by Goutam Mukherjee Pdf

Contributed lectures presented earlier at Winter School on Transformation Groups.

Author : V. M. Buchstaber,Taras E. Panov
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 48,5 Mb
Release : 2002
Category : Combinatorial analysis
ISBN : 9780821831861

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Torus Actions and Their Applications in Topology and Combinatorics by V. M. Buchstaber,Taras E. Panov Pdf

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 : Victor M. Buchstaber,Taras E. Pano
Publisher : American Mathematical Soc.
Page : 518 pages
File Size : 46,7 Mb
Release : 2015-07-15
Category : Algebraic topology
ISBN : 9781470422141

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Toric Topology by Victor M. Buchstaber,Taras E. Pano Pdf

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.

Author : Alvaro Pelayo
Publisher : Unknown
Page : 81 pages
File Size : 55,9 Mb
Release : 2010
Category : MATHEMATICS
ISBN : 1470405733

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Symplectic Actions of 2-tori on 4-manifolds by Alvaro Pelayo Pdf

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 44,6 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

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 : International Conference on Toric Topology
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 54,9 Mb
Release : 2008
Category : Topology
ISBN : 9780821844861

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Toric Topology by International Conference on Toric Topology Pdf

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 : Augustin Banyaga,Djideme F Houenou
Publisher : World Scientific
Page : 180 pages
File Size : 44,7 Mb
Release : 2016-08-08
Category : Electronic
ISBN : 9789814696722

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A Brief Introduction to Symplectic and Contact Manifolds by Augustin Banyaga,Djideme F Houenou Pdf

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. Contents: Symplectic Vector SpacesSymplectic ManifoldsHamiltonian Systems and Poisson AlgebraGroup ActionsContact ManifoldsSolutions of Selected ExercisesEpilogue: The C0-Symplectic and Contact Topology Readership: Graduate students, researchers and more advanced mathematicians. Symplectic;Contact GeometryKey Features: It is briefThe easy part has been tested and been used for a short courseThe advanced material develops things related to one of the author's research furtherThere is no book, going from the very elementary part to the very advanced level, like this one

Author : Dusa McDuff,Dietmar Salamon
Publisher : Oxford University Press
Page : 637 pages
File Size : 55,7 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198794899

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Introduction to Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date.

Author : Ga.) Georgia International Topology Conference (2001 : Athens
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 50,5 Mb
Release : 2003
Category : Differential topology
ISBN : 9780821835074

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Topology and Geometry of Manifolds by Ga.) Georgia International Topology Conference (2001 : Athens Pdf

Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.

Author : Jacques Hurtubise,François Lalonde
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 50,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401716673

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Gauge Theory and Symplectic Geometry by Jacques Hurtubise,François Lalonde Pdf

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.

Author : Shubham Dwivedi,Jonathan Herman,Lisa C. Jeffrey,Theo van den Hurk
Publisher : Springer Nature
Page : 132 pages
File Size : 52,8 Mb
Release : 2019-09-23
Category : Mathematics
ISBN : 9783030272272

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Hamiltonian Group Actions and Equivariant Cohomology by Shubham Dwivedi,Jonathan Herman,Lisa C. Jeffrey,Theo van den Hurk Pdf

This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.

Author : Alvaro Pelayo
Publisher : Unknown
Page : 574 pages
File Size : 52,6 Mb
Release : 2007
Category : Electronic
ISBN : UOM:39015070903227

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Symplectic Torus Actions by Alvaro Pelayo Pdf

Author : Alvaro Pelayo
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 43,7 Mb
Release : 2010-02-22
Category : Mathematics
ISBN : 9780821847138

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Symplectic Actions of $2$-Tori on $4$-Manifolds by Alvaro Pelayo Pdf

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.