The Topology Of Torus Actions On Symplectic Manifolds

Author : Michèle Audin
Publisher : Birkhäuser
ISBN 13 : 3034872216
Total Pages : 181 pages
Book Rating : 4.18/5 ( download)

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Download or read book The Topology of Torus Actions on Symplectic Manifolds written by Michèle Audin and published by Birkhäuser. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 3034879601
Total Pages : 331 pages
Book Rating : 4.06/5 ( download)

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Download or read book Torus Actions on Symplectic Manifolds written by Michèle Audin and published by Birkhäuser. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 9386279304
Total Pages : 140 pages
Book Rating : 4.09/5 ( download)

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Download or read book Transformation Groups written by Goutam Mukherjee and published by Springer. This book was released on 2005-04-15 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed lectures presented earlier at Winter School on Transformation Groups.

Author : Milena Dorota Pabiniak
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.41/5 ( download)

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Download or read book Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology written by Milena Dorota Pabiniak and published by . This book was released on 2012 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : V. M. Buchstaber
Publisher : American Mathematical Soc.
ISBN 13 : 0821831860
Total Pages : 154 pages
Book Rating : 4.61/5 ( download)

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Download or read book Torus Actions and Their Applications in Topology and Combinatorics written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 2002 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alvaro Pelayo
Publisher :
ISBN 13 : 9781470405731
Total Pages : 81 pages
Book Rating : 4.33/5 ( download)

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Download or read book Symplectic Actions of 2-tori on 4-manifolds written by Alvaro Pelayo and published by . This book was released on 2010 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ana Cannas da Silva
Publisher : Springer
ISBN 13 : 354045330X
Total Pages : 240 pages
Book Rating : 4.07/5 ( download)

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Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Victor M. Buchstaber
Publisher : American Mathematical Soc.
ISBN 13 : 147042214X
Total Pages : 534 pages
Book Rating : 4.41/5 ( download)

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Download or read book Toric Topology written by Victor M. Buchstaber and published by American Mathematical Soc.. This book was released on 2015-07-15 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Augustin Banyaga
Publisher : World Scientific
ISBN 13 : 9814696722
Total Pages : 178 pages
Book Rating : 4.22/5 ( download)

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Download or read book A Brief Introduction To Symplectic And Contact Manifolds written by Augustin Banyaga and published by World Scientific. This book was released on 2016-08-08 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Yakov Eliashberg
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886892
Total Pages : 452 pages
Book Rating : 4.94/5 ( download)

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Download or read book Symplectic Geometry and Topology written by Yakov Eliashberg and published by American Mathematical Soc.. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.