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Author | : Stephan C. Carlson |
Publisher | : John Wiley & Sons |
Total Pages | : 178 |
Release | : 2001-01-10 |
Genre | : Mathematics |
ISBN | : |
Download Topology of Surfaces, Knots, and Manifolds Book in PDF, ePub and Kindle
This textbook contains ideas and problems involving curves, surfaces, and knots, which make up the core of topology. Carlson (mathematics, Rose-Hulman Institute of Technology) introduces some basic ideas and problems concerning manifolds, especially one- and two- dimensional manifolds. A sampling of topics includes classification of compact surfaces, putting more structure on the surfaces, graphs and topology, and knot theory. It is assumed that the reader has a background in calculus. Annotation copyrighted by Book News Inc., Portland, OR.
Author | : Johanna Adison |
Publisher | : |
Total Pages | : 280 |
Release | : 2016-10-01 |
Genre | : |
ISBN | : 9781681176543 |
Download Topology of Surfaces, Knots, and Manifolds Book in PDF, ePub and Kindle
Since the early part of the 20th century both topology and analysis have fed off each other and this has resulted in some very beautiful theorems that lie at the interface between these two disciplines. Perhaps the best known example of these is Brouwer's fixed point theorem (later generalised by J. Schauder to more general spaces) which has had countless applications in applied mathematics, economics and analysis itself. Topology is the study of those properties of objects that are preserved under careful deformation. Topology is the area of mathematics which investigates continuity and related concepts. Important fundamental notions soon to come are for example open and closed sets, continuity, and homeomorphism. Originally coming from questions in analysis and differential geometry, by now topology permeates mostly every field of math including algebra, combinatorics, logic, and plays a fundamental role in algebraic/arithmetic geometry as we know it today. s Topology of Surfaces, Knots, and Manifolds offers an intuition-based and applied approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A comprehensive, self-contained treatment presenting general results of the theory.
Author | : Viktor Vasilʹevich Prasolov |
Publisher | : American Mathematical Soc. |
Total Pages | : 250 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821808982 |
Download Knots, Links, Braids and 3-Manifolds Book in PDF, ePub and Kindle
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 | : L.Christine Kinsey |
Publisher | : Springer Science & Business Media |
Total Pages | : 290 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208998 |
Download Topology of Surfaces Book in PDF, ePub and Kindle
" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.
Author | : Seiichi Kamada |
Publisher | : Springer |
Total Pages | : 212 |
Release | : 2017-03-28 |
Genre | : Mathematics |
ISBN | : 9811040915 |
Download Surface-Knots in 4-Space Book in PDF, ePub and Kindle
This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.
Author | : Vassily Olegovich Manturov |
Publisher | : World Scientific |
Total Pages | : 541 |
Release | : 2015-01-27 |
Genre | : Mathematics |
ISBN | : 9814630632 |
Download New Ideas In Low Dimensional Topology Book in PDF, ePub and Kindle
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 | : Scott Carter |
Publisher | : Springer Science & Business Media |
Total Pages | : 234 |
Release | : 2004-04-05 |
Genre | : Mathematics |
ISBN | : 9783540210405 |
Download Surfaces in 4-Space Book in PDF, ePub and Kindle
This book discusses knotted surfaces in 4-dimensional space and surveys many of the known results, including knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory.
Author | : Ruben Vigara Benito |
Publisher | : World Scientific |
Total Pages | : 299 |
Release | : 2016-03-11 |
Genre | : Mathematics |
ISBN | : 9814725501 |
Download Representing 3-manifolds By Filling Dehn Surfaces Book in PDF, ePub and Kindle
This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.
Author | : Jennifer Schultens |
Publisher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 2014-05-21 |
Genre | : Mathematics |
ISBN | : 1470410206 |
Download Introduction to 3-Manifolds Book in PDF, ePub and Kindle
This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Author | : Colin Conrad Adams |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821836781 |
Download The Knot Book Book in PDF, ePub and Kindle
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.