Low Dimensional Topology

Author : Javier Fernández de Bobadilla,Tamás László,András Stipsicz
Publisher : Springer Nature
Page : 332 pages
File Size : 54,6 Mb
Release : 2021-05-27
Category : Mathematics
ISBN : 9783030619589

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Singularities and Their Interaction with Geometry and Low Dimensional Topology by Javier Fernández de Bobadilla,Tamás László,András Stipsicz Pdf

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Author : Colin C. Adams,Cameron McA. Gordon,Vaughan F.R. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Przytycki,Renzo Ricca,Radmila Sazdanovic
Publisher : Springer
Page : 476 pages
File Size : 45,6 Mb
Release : 2019-06-26
Category : Mathematics
ISBN : 9783030160319

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Knots, Low-Dimensional Topology and Applications by Colin C. Adams,Cameron McA. Gordon,Vaughan F.R. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Przytycki,Renzo Ricca,Radmila Sazdanovic Pdf

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Author : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 41,5 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9780821848166

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Low-Dimensional Geometry by Francis Bonahon Pdf

The 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.

Author : Tomasz Mrowka,Peter Steven Ozsváth
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 50,9 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780821886960

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Low Dimensional Topology by Tomasz Mrowka,Peter Steven Ozsváth Pdf

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.

Author : Olivier Collin,Stefan Friedl,Cameron Gordon,Stephan Tillmann,Liam Watson
Publisher : American Mathematical Soc.
Page : 353 pages
File Size : 51,5 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470452094

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Characters in Low-Dimensional Topology by Olivier Collin,Stefan Friedl,Cameron Gordon,Stephan Tillmann,Liam Watson Pdf

This volume contains the proceedings of a conference celebrating the work of Steven Boyer, held from June 2–6, 2018, at Université du Québec à Montréal, Montréal, Québec, Canada. Boyer's contributions to research in low-dimensional geometry and topology, and to the Canadian mathematical community, were recognized during the conference. The articles cover a broad range of topics related, but not limited, to the topology and geometry of 3-manifolds, properties of their fundamental groups and associated representation varieties.

Author : Vassily Olegovich Manturov,Louis H Kauffman
Publisher : World Scientific
Page : 540 pages
File Size : 47,7 Mb
Release : 2015-01-27
Category : Mathematics
ISBN : 9789814630634

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New Ideas In Low Dimensional Topology by Vassily Olegovich Manturov,Louis H Kauffman Pdf

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.

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 42,7 Mb
Release : 2006
Category : Mathematics
ISBN : 0821838458

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Floer Homology, Gauge Theory, and Low-Dimensional Topology by Clay Mathematics Institute. Summer School Pdf

Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).

Author : Michael H. Freedman,Feng Luo
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 53,7 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821870006

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Selected Applications of Geometry to Low-Dimensional Topology by Michael H. Freedman,Feng Luo Pdf

Based 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.

Author : Nikolai Saveliev
Publisher : Walter de Gruyter
Page : 212 pages
File Size : 52,6 Mb
Release : 2012-10-25
Category : Mathematics
ISBN : 9783110806359

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Lectures on the Topology of 3-Manifolds by Nikolai Saveliev Pdf

Author : Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 55,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821808986

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Knots, Links, Braids and 3-Manifolds by Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ Pdf

This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.

Author : William P. Thurston
Publisher : Princeton University Press
Page : 340 pages
File Size : 47,7 Mb
Release : 1997
Category : Mathematics
ISBN : 0691083045

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Three-dimensional Geometry and Topology by William P. Thurston Pdf

Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.

Author : R. Brown,T. L. Thickstun
Publisher : Cambridge University Press
Page : 261 pages
File Size : 51,8 Mb
Release : 1982-05-20
Category : Mathematics
ISBN : 9780521281461

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Low-Dimensional Topology by R. Brown,T. L. Thickstun Pdf

This 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.

Author : J. Scott Carter
Publisher : World Scientific
Page : 398 pages
File Size : 53,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770967

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Intelligence of Low Dimensional Topology 2006 by J. Scott Carter Pdf

This volume gathers the contributions from the international conference Intelligence of Low Dimensional Topology 2006, which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.

Author : Alexandru Scorpan
Publisher : American Mathematical Society
Page : 614 pages
File Size : 53,6 Mb
Release : 2022-01-26
Category : Mathematics
ISBN : 9781470468613

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The Wild World of 4-Manifolds by Alexandru Scorpan Pdf

What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. —MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. — Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.

Author : A Banyaga,H Movahedi-Lankarani,R Wells
Publisher : World Scientific
Page : 136 pages
File Size : 50,8 Mb
Release : 1999-10-15
Category : Electronic
ISBN : 9789814543439

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Topics in Low-Dimensional Topology by A Banyaga,H Movahedi-Lankarani,R Wells Pdf

Recent success with the four-dimensional Poincaré conjecture has revived interest in low-dimensional topology, especially the three-dimensional Poincaré conjecture and other aspects of the problems of classifying three-dimensional manifolds. These problems have a driving force, and have generated a great body of research, as well as insight. The main topics treated in this book include a paper by V Poenaru on the Poincaré conjecture and its ramifications, giving an insight into the herculean work of the author on the subject. Steve Armentrout's paper on “Bing's dogbone space” belongs to the topics in three-dimensional topology motivated by the Poincaré conjecture. S Singh gives a nice synthesis of Armentrout's work. Also included in the volume are shorter original papers, dealing with somewhat different aspects of geometry, and dedicated to Armentrout by his colleagues — Augustin Banyaga (and Jean-Pierre Ezin), David Hurtubise, Hossein Movahedi-Lankarani and Robert Wells. Contents: Mathematics of Steve Armentrout: A Review (S Singh)Bing's Dogbone Space Is Not Strongly Locally Simply Connected (S Armentrout)A Program for the Poincaré Conjecture and Some of Its Ramifications (V Poénaru)On the Foundation of Geometry, Analysis, and the Differentiable Structure for Manifolds (D Sullivan)A Conformal Invariant Characterizing the Sphere (A Banyaga & J-P Ezin)Spaces of Holomorphic Maps from ∀P1 to Complex Grassmann Manifolds (D E Hurtubise)Sets with Lie Isometry Groups (H Movahedi-Lankarani & R Wells) Readership: Researchers in mathematics and physics. Keywords:Poincare Conjecture;Topology;Holomorphic Maps;Complex Grassmann Manifolds;Lie Isometry Groups