Geometry and Topology of Low Dimensional Systems
Author: T. R. Govindarajan
Publisher: Springer Nature
Published:
Total Pages: 174
ISBN-13: 3031595017
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Geometry and Topology of Low Dimensional Systems
Author: Ramadevi Pichai
Publisher: Springer
Published: 2024-07-11
Total Pages: 0
ISBN-13: 9783031595004
DOWNLOAD EBOOKThis book introduces the field of topology, a branch of mathematics that explores the properties of geometric space, with a focus on low-dimensional systems. The authors discuss applications in various areas of physics. The first chapters of the book cover the formal aspects of topology, including classes, homotopic groups, metric spaces, and Riemannian and pseudo-Riemannian geometry. These topics are essential for understanding the theoretical concepts and notations used in the next chapters of the book. The applications encompass defects in crystalline structures, space topology, spin statistics, Braid group, Chern-Simons field theory, and 3D gravity, among others. This self-contained book provides all the necessary additional material for both physics and mathematics students. The presentation is enriched with examples and exercises, making it accessible for readers to grasp the concepts with ease. The authors adopt a pedagogical approach, posing many unsolved questions in simple situations that can serve as challenging projects for students. Suitable for a one-semester postgraduate level course, this text is ideal for teaching purposes.
Selected Applications of Geometry to Low-Dimensional Topology
Author: Michael H. Freedman
Publisher: American Mathematical Soc.
Published: 1990
Total Pages: 93
ISBN-13: 0821870009
DOWNLOAD EBOOKBased on lectures presented at Pennsylvania State University in February 1987, this work begins with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceeds to the topology and geometry of foliated 3-manifolds. It also explains why four-dimensional space has special attributes.
The Geometry and Topology of Change-ordered Quantum Fields in Low-dimensional Systems
Author: Felix Flicker
Publisher:
Published: 2015
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKLow Dimensional Topology
Author: Tomasz Mrowka
Publisher: American Mathematical Soc.
Published: 2009-01-01
Total Pages: 331
ISBN-13: 0821886967
DOWNLOAD EBOOKLow-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.
New Ideas In Low Dimensional Topology
Author: Vassily Olegovich Manturov
Publisher: World Scientific
Published: 2015-01-27
Total Pages: 541
ISBN-13: 9814630632
DOWNLOAD EBOOKThis 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.
Low-Dimensional Topology
Author: R. Brown
Publisher: Cambridge University Press
Published: 1982-05-20
Total Pages: 261
ISBN-13: 0521281466
DOWNLOAD EBOOKThis volume consists of the proceedings of a conference held at the University College of North Wales (Bangor) in July of 1979. It assembles research papers which reflect diverse currents in low-dimensional topology. The topology of 3-manifolds, hyperbolic geometry and knot theory emerge as major themes. The inclusion of surveys of work in these areas should make the book very useful to students as well as researchers.
Low Dimensional Topology
Author: American Mathematical Society
Publisher: American Mathematical Soc.
Published: 1983
Total Pages: 358
ISBN-13: 0821850164
DOWNLOAD EBOOKDerived from a special session on Low Dimensional Topology organized and conducted by Dr Lomonaco at the American Mathematical Society meeting held in San Francisco, California, January 7-11, 1981.
Low-Dimensional Geometry
Author: Francis Bonahon
Publisher: American Mathematical Soc.
Published: 2009-07-14
Total Pages: 403
ISBN-13: 082184816X
DOWNLOAD EBOOKThe study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.
Low-dimensional and Symplectic Topology
Author: Michael Usher
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 242
ISBN-13: 0821852353
DOWNLOAD EBOOKEvery 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.
