Low-dimensional and Symplectic Topology

2011 Mathematics

Author : Michael Usher
Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 353/5 ( reviews)

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Book Synopsis Low-dimensional and Symplectic Topology by : Michael Usher

Download or read book Low-dimensional and Symplectic Topology written by Michael Usher. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Every eight years since 1961, the University of Georgia has hosted a major international topology conference aimed at disseminating important recent results and bringing together researchers at different stages of their careers. This volume contains the proceedings of the 2009 conference, which includes survey and research articles concerning such areas as knot theory, contact and symplectic topology, 3-manifold theory, geometric group theory, and equivariant topology. Among other highlights of the volume, a survey article by Stefan Friedl and Stefano Vidussi provides an accessible treatment of their important proof of Taubes' conjecture on symplectic structures on the product of a 3-manifold and a circle, and an intriguing short article by Dennis Sullivan opens the door to the use of modern algebraic-topological techniques in the study of finite-dimensional models of famously difficult problems in fluid dynamics. Continuing what has become a tradition, this volume contains a report on a problem session held at the conference, discussing a variety of open problems in geometric topology.

Holomorphic Curves in Low Dimensions

2018-06-28 Mathematics

Author : Chris Wendl
Release : 2018-06-28
Genre : Mathematics
Kind : eBook
Book Rating : 719/5 ( reviews)

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Book Synopsis Holomorphic Curves in Low Dimensions by : Chris Wendl

Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl. This book was released on 2018-06-28. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

New Ideas In Low Dimensional Topology

2015-01-27 Mathematics

Author : Vassily Olegovich Manturov
Release : 2015-01-27
Genre : Mathematics
Kind : eBook
Book Rating : 632/5 ( reviews)

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Book Synopsis New Ideas In Low Dimensional Topology by : Vassily Olegovich Manturov

Download or read book New Ideas In Low Dimensional Topology written by Vassily Olegovich Manturov. This book was released on 2015-01-27. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.

Research Directions in Symplectic and Contact Geometry and Topology

2022-02-02 Mathematics

Author : Bahar Acu
Release : 2022-02-02
Genre : Mathematics
Kind : eBook
Book Rating : 79X/5 ( reviews)

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Book Synopsis Research Directions in Symplectic and Contact Geometry and Topology by : Bahar Acu

Download or read book Research Directions in Symplectic and Contact Geometry and Topology written by Bahar Acu. This book was released on 2022-02-02. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this area. The papers were written with a broad audience in mind so as to reach a wide range of mathematicians at various levels. Aside from teaching readers about developing research areas, this book will inspire researchers to ask further questions to continue to advance the field. The volume contains both original results and survey articles, presenting the results of collaborative research on a wide range of topics. These projects began at the Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon) in July 2019 at ICERM, Brown University. Each group of authors included female and nonbinary mathematicians at different career levels in mathematics and with varying areas of expertise. This paved the way for new connections between mathematicians at all career levels, spanning multiple continents, and resulted in the new collaborations and directions that are featured in this work.

Low Dimensional Topology

2009-01-01 Mathematics

Author : Tomasz Mrowka
Release : 2009-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 967/5 ( reviews)

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Book Synopsis Low Dimensional Topology by : Tomasz Mrowka

Download or read book Low Dimensional Topology written by Tomasz Mrowka. This book was released on 2009-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.

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