Topology of Surfaces, Knots, and Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology of Surfaces, Knots, and Manifolds write by Stephan C. Carlson. This book was released on 2001-01-10. Topology of Surfaces, Knots, and Manifolds available 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.
Topology of Surfaces, Knots, and Manifolds
Topology of Surfaces, Knots, and Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology of Surfaces, Knots, and Manifolds write by Johanna Adison. This book was released on 2016-10-01. Topology of Surfaces, Knots, and Manifolds available 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.
Topology of Surfaces
Topology of Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology of Surfaces write by L.Christine Kinsey. This book was released on 1997-09-26. Topology of Surfaces available 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.
Knots, Links, Braids and 3-Manifolds
Knots, Links, Braids and 3-Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Knots, Links, Braids and 3-Manifolds write by Viktor Vasilʹevich Prasolov. This book was released on 1997. Knots, Links, Braids and 3-Manifolds available 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.
Surface-Knots in 4-Space
Surface-Knots in 4-Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Surface-Knots in 4-Space write by Seiichi Kamada. This book was released on 2017-03-28. Surface-Knots in 4-Space available 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.
