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.
Surfaces in 4-Space
Surfaces 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 Surfaces in 4-Space write by Scott Carter. This book was released on 2013-06-29. Surfaces in 4-Space available in PDF, EPUB and Kindle. Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.
Knotted Surfaces and Their Diagrams
Knotted Surfaces and Their Diagrams - 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 Knotted Surfaces and Their Diagrams write by J. Scott Carter. This book was released on 2023-12-06. Knotted Surfaces and Their Diagrams available in PDF, EPUB and Kindle. In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts. The authors show how to unknot intricate examples using these moves. The third chapter reviews the braid theory of knotted surfaces. Examples of the Alexander isotopy are given, and the braid movie moves are presented. In the fourth chapter, properties of the projections of knotted surfaces are studied. Oriented surfaces in 4-space are shown to have planar projections without cusps and without branch points. Signs of triple points are studied. Applications of triple-point smoothing that include proofs of triple-point formulas and a proof of Whitney's congruence on normal Euler classes are presented. The fifth chapter indicates how to obtain presentations for the fundamental group and the Alexander modules. Key examples are worked in detail. The Seifert algorithm for knotted surfaces is presented and exemplified. The sixth chapter relates knotted surfaces and diagrammatic techniques to 2-categories. Solutions to the Zamolodchikov equations that are diagrammatically obtained are presented. The book contains over 200 illustrations that illuminate the text. Examples are worked out in detail, and readers have the opportunity to learn first-hand a series of remarkable geometric techniques.
How Surfaces Intersect in Space
How Surfaces Intersect in 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 How Surfaces Intersect in Space write by J. Scott Carter. This book was released on 1995. How Surfaces Intersect in Space available in PDF, EPUB and Kindle. This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.
Knotted Surfaces and Their Diagrams
Knotted Surfaces and Their Diagrams - 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 Knotted Surfaces and Their Diagrams write by J. Scott Carter, Masahico Saito. This book was released on . Knotted Surfaces and Their Diagrams available in PDF, EPUB and Kindle.
