Differential And Low Dimensional Topology

Author : András Juhász
Publisher : Cambridge University Press
Page : 240 pages
File Size : 51,7 Mb
Release : 2023-03-31
Category : Mathematics
ISBN : 9781009220583

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Differential and Low-Dimensional Topology by András Juhász Pdf

The new student in differential and low-dimensional topology is faced with a bewildering array of tools and loosely connected theories. This short book presents the essential parts of each, enabling the reader to become 'literate' in the field and begin research as quickly as possible. The only prerequisite assumed is an undergraduate algebraic topology course. The first half of the text reviews basic notions of differential topology and culminates with the classification of exotic seven-spheres. It then dives into dimension three and knot theory. There then follows an introduction to Heegaard Floer homology, a powerful collection of modern invariants of three- and four-manifolds, and of knots, that has not before appeared in an introductory textbook. The book concludes with a glimpse of four-manifold theory. Students will find it an exhilarating and authoritative guide to a broad swathe of the most important topics in modern topology.

Author : Vassily Olegovich Manturov,Louis H Kauffman
Publisher : World Scientific
Page : 540 pages
File Size : 49,5 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 : Tomasz Mrowka,Peter Steven Ozsváth
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 55,5 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 : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 44,9 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 : Hugh Osborn
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 44,9 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489916129

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Low-Dimensional Topology and Quantum Field Theory by Hugh Osborn Pdf

The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics.

Author : Samuel J. Lomonaco
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 55,6 Mb
Release : 1983
Category : Mathematics
ISBN : 9780821850169

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Low Dimensional Topology by Samuel J. Lomonaco Pdf

This volume arose 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.

Author : Michael H. Freedman,Feng Luo
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 43,7 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 : R. Brown,T. L. Thickstun
Publisher : Cambridge University Press
Page : 261 pages
File Size : 53,5 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 : Olivier Collin,Stefan Friedl,Cameron Gordon,Stephan Tillmann,Liam Watson
Publisher : American Mathematical Soc.
Page : 353 pages
File Size : 55,6 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 : J. Scott Carter
Publisher : World Scientific
Page : 398 pages
File Size : 44,7 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 : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 51,6 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 : Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 44,6 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 : Roger Fenn
Publisher : Unknown
Page : 0 pages
File Size : 45,9 Mb
Release : 1985
Category : Electronic
ISBN : OCLC:859818574

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Low-dimensional Topology by Roger Fenn Pdf

Author : Peter Kronheimer,Tomasz Mrowka
Publisher : Unknown
Page : 796 pages
File Size : 47,9 Mb
Release : 2007-12-20
Category : Mathematics
ISBN : 052188022X

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Monopoles and Three-Manifolds by Peter Kronheimer,Tomasz Mrowka Pdf

This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.

Author : Daniel S. Freed,Karen K. Uhlenbeck
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397038

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Instantons and Four-Manifolds by Daniel S. Freed,Karen K. Uhlenbeck Pdf

From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I would strongly advise the graduate student or working mathematician who wishes to learn the analytic aspects of this subject to begin with Freed and Uhlenbeck's book." #Bulletin of the American Mathematical Society#2