Two-Bridge Knots Have Property $\mathbf {P}$ PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Two-Bridge Knots Have Property $\mathbf {P}$ PDF full book. Access full book title Two-Bridge Knots Have Property $\mathbf {P}$ by Moto-o Takahashi. Download full books in PDF and EPUB format.
Author: Moto-o Takahashi
Publisher: American Mathematical Soc.
ISBN: 082182239X
Category : Mathematics
Languages : en
Pages : 112
Get Book Here
Book Description
A knot K is said to have Property P if simply-connected 3-manifolds cannot be obtained by non-trivial Dehn surgeries along K. Torus knots, twist knots, a class of 2-bridge knots, and 2-bridge knots with 9 or fewer crossings are known to have Property P. On the other hand, Ochiai proves that the 3-sphere cannot be obtained by a non-trivial surgery along a two-bridge knot. In this monograph we shall prove that every non-trivial two-bridge knot has Property P. In the proof we shall use Bezout's theorem in algebraic geometry.
Author: Moto-o Takahashi
Publisher: American Mathematical Soc.
ISBN: 082182239X
Category : Mathematics
Languages : en
Pages : 112
Get Book Here
Book Description
A knot K is said to have Property P if simply-connected 3-manifolds cannot be obtained by non-trivial Dehn surgeries along K. Torus knots, twist knots, a class of 2-bridge knots, and 2-bridge knots with 9 or fewer crossings are known to have Property P. On the other hand, Ochiai proves that the 3-sphere cannot be obtained by a non-trivial surgery along a two-bridge knot. In this monograph we shall prove that every non-trivial two-bridge knot has Property P. In the proof we shall use Bezout's theorem in algebraic geometry.
Author: John McCleary
Publisher: The Mathematical Association of America
ISBN: 0883856522
Category : Mathematics
Languages : en
Pages : 289
Get Book Here
Book Description
Hover over the image to zoom. Click the image for a popup.Email a Friend About This ItemLogin to Submit a Review inShare John McCleary In Exercises in (Mathematical) Style, the author investigates the world of that familiar set of numbers, the binomial coefficients. While the reader learns some of the properties, relations, and generalizations of the numbers of Pascal's triangle, each story explores a different mode of discourse - from arguing algebraically, combinatorially, geometrically, or by induction, contradiction, or recursion to discovering mathematical facts in poems, music, letters, and various styles of stories. The author follows the example of Raymond Queneau's Exercises in Style, giving the reader 99 stories in various styles. The ubiquitous nature of binomial coefficients leads the tour through combinatorics, number theory, algebra, analysis, and even topology. The book celebrates the joy of writing and the joy of mathematics, found by engaging the rich properties of this simple set of numbers.
Author: Jessica S. Purcell
Publisher: American Mathematical Soc.
ISBN: 1470454998
Category : Education
Languages : en
Pages : 392
Get Book Here
Book Description
This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.
Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
Get Book Here
Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: Slavik V. Jablan
Publisher: World Scientific
ISBN: 9812772235
Category : Mathematics
Languages : en
Pages : 497
Get Book Here
Book Description
LinKnot - Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics. The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves. Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 432
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Automobiles
Languages : en
Pages : 942
Get Book Here
Book Description
Vol. 29, no. 8-37, no. 7 (Aug., 1937-July, 1944) include the section: Aviation.
Author: Ulrich Daepp
Publisher: Springer Science & Business Media
ISBN: 0387215603
Category : Mathematics
Languages : en
Pages : 391
Get Book Here
Book Description
This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.
Author: James Aitken Wylie
Publisher:
ISBN:
Category :
Languages : en
Pages : 652
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 436
Get Book Here
Book Description
