Knots and Primes - 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 and Primes write by Masanori Morishita. This book was released on 2011-11-27. Knots and Primes available in PDF, EPUB and Kindle. This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
Knots and Primes
Knots and Primes - 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 and Primes write by Masanori Morishita. This book was released on . Knots and Primes available in PDF, EPUB and Kindle.
Primes and Knots
Primes and Knots - 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 Primes and Knots write by Toshitake Kohno. This book was released on 2006. Primes and Knots available in PDF, EPUB and Kindle. This volume deals systematically with connections between algebraic number theory and low-dimensional topology. Of particular note are various inspiring interactions between number theory and low-dimensional topology discussed in most papers in this volume. For example, quite interesting are the use of arithmetic methods in knot theory and the use of topological methods in Galois theory. Also, expository papers in both number theory and topology included in the volume can help a wide group of readers to understand both fields as well as the interesting analogies and relations that bring them together.
The Knot Book
The Knot Book - 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 The Knot Book write by Colin Conrad Adams. This book was released on 2004. The Knot Book available 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.
Knots and Links
Knots and Links - 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 and Links write by Dale Rolfsen. This book was released on 2003. Knots and Links available in PDF, EPUB and Kindle. Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
