Symplectic And Contact Topology Interactions And Perspectives

Author : Y. Eliashberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821831623
Total Pages : 210 pages
Book Rating : 4.25/5 ( download)

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Download or read book Symplectic and Contact Topology: Interactions and Perspectives written by Y. Eliashberg and published by American Mathematical Soc.. This book was released on 2003 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume are written by participants of the ``Symplectic and Contact Topology, Quantum Cohomology, and Symplectic Field Theory'' symposium. The workshop was part of a semester-long joint venture of The Fields Institute in Toronto and the Centre de Recherches Mathematiques in Montreal. The twelve papers cover the following topics: Symplectic Topology, the interaction between symplectic and other geometric structures, and Differential Geometry and Topology. The Proceeding concludes with two papers that have a more algebraic character. One is related to the program of Homological Mirror Symmetry: the author defines a category of extended complex manifolds and studies its properties. The subject of the final paper is Non-commutative Symplectic Geometry, in particular the structure of the symplectomorphism group of a non-commutative complex plane. The in-depth articles make this book a useful reference for graduate students as well as research mathematicians.

Author : Frédéric Bourgeois
Publisher : Springer Science & Business Media
ISBN 13 : 3319020366
Total Pages : 538 pages
Book Rating : 4.65/5 ( download)

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Download or read book Contact and Symplectic Topology written by Frédéric Bourgeois and published by Springer Science & Business Media. This book was released on 2014-03-10 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

Author : Hansjörg Geiges
Publisher : Cambridge University Press
ISBN 13 : 1139467956
Total Pages : 8 pages
Book Rating : 4.57/5 ( download)

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Download or read book An Introduction to Contact Topology written by Hansjörg Geiges and published by Cambridge University Press. This book was released on 2008-03-13 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.

Author : Masoud Khalkhali
Publisher : American Mathematical Soc.
ISBN 13 : 0821848496
Total Pages : 176 pages
Book Rating : 4.94/5 ( download)

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Download or read book Perspectives on Noncommutative Geometry written by Masoud Khalkhali and published by American Mathematical Soc.. This book was released on 2011 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.

Author :
Publisher :
ISBN 13 :
Total Pages : 768 pages
Book Rating : 4.30/5 ( download)

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Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Society for Mathematical Biology. Conference
Publisher : American Mathematical Soc.
ISBN 13 : 0821848453
Total Pages : 145 pages
Book Rating : 4.56/5 ( download)

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Download or read book New Perspectives in Mathematical Biology written by Society for Mathematical Biology. Conference and published by American Mathematical Soc.. This book was released on 2010 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an overview of the distinct variety and diversity of current research in this field. In every chapter of this book, which covers themes ranging from cancer modelling to infectious diseases to orthopaedics and musculoskeletal tissue mechanics, there is clear evidence of the strong connections and interactions of mathematics with the biological and biomedical sciences that have spawned new models and novel insights.

Author : François Charest
Publisher : American Mathematical Society
ISBN 13 : 147045310X
Total Pages : 178 pages
Book Rating : 4.07/5 ( download)

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Download or read book Floer Cohomology and Flips written by François Charest and published by American Mathematical Society. This book was released on 2022-08-31 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Jonny Evans
Publisher : Cambridge University Press
ISBN 13 : 1009372661
Total Pages : 242 pages
Book Rating : 4.64/5 ( download)

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Download or read book Lectures on Lagrangian Torus Fibrations written by Jonny Evans and published by Cambridge University Press. This book was released on 2023-07-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.

Author : Hans U. Boden
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871492
Total Pages : 368 pages
Book Rating : 4.98/5 ( download)

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Download or read book Geometry and Topology of Manifolds written by Hans U. Boden and published by American Mathematical Soc.. This book was released on with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory, Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the many excellent talks delivered at the conference.

Author : Erhard Neher
Publisher : American Mathematical Soc.
ISBN 13 : 082185237X
Total Pages : 226 pages
Book Rating : 4.78/5 ( download)

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Download or read book Geometric Representation Theory and Extended Affine Lie Algebras written by Erhard Neher and published by American Mathematical Soc.. This book was released on 2011 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.