Special Issue Knots In Hellas 98 PDF Download
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| Author | : C. McA. Gordon |
| Publisher | : World Scientific |
| Total Pages | : 580 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9810243405 |
Download Knots in Hellas '98 Book in PDF, ePub and Kindle
There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon?Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2, C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.
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| Release | : 2001 |
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Download Special issue Knots in Hellas '98 Book in PDF, ePub and Kindle
| Author | : Jorge Alberto Calvo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 356 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 082183200X |
Download Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$ Book in PDF, ePub and Kindle
The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.
| Author | : S. Chmutov |
| Publisher | : Cambridge University Press |
| Total Pages | : 521 |
| Release | : 2012-05-24 |
| Genre | : Mathematics |
| ISBN | : 1107020832 |
Download Introduction to Vassiliev Knot Invariants Book in PDF, ePub and Kindle
A detailed exposition of the theory with an emphasis on its combinatorial aspects.
| Author | : Vassily Olegovich Manturov |
| Publisher | : World Scientific |
| Total Pages | : 387 |
| Release | : 2020-04-22 |
| Genre | : Mathematics |
| ISBN | : 9811220131 |
Download Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory Book in PDF, ePub and Kindle
This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.
| Author | : Jack Shulman Avrin |
| Publisher | : World Scientific |
| Total Pages | : 281 |
| Release | : 2021-08-06 |
| Genre | : Science |
| ISBN | : 9813278994 |
Download On Complementarity: A Universal Organizing Principle Book in PDF, ePub and Kindle
It is not uncommon for the Principle of Complementarity to be invoked in either Science or Philosophy, viz. the ancient oriental philosophy of Yin and Yang whose symbolic representation is portrayed on the cover of the book. Or Niels Bohr's use of it as the basis for the so-called Copenhagen interpretation of Quantum Mechanics. This book arose as an outgrowth of the author's previous book entitled 'Knots, Braids and Moebius Strips,' published by World Scientific in 2015, wherein the Principle itself was discovered to be expressible as a simple 2x2 matrix that summarizes the algebraic essence of both the well-known Microbiology of DNA and the author's version of the elementary particles of physics. At that point, the possibility of an even wider utilization of that expression of Complementarity arose.The current book, features Complementarity, in which the matrix algebra is extended to characterize not only DNA itself but the well-known process of its replication, a most gratifying outcome. The book then goes on to explore Complementarity, with and without its matrix expression, as it occurs, not only in much of physics but in its extension to cosmology as well.
| Author | : Alexey Stakhov |
| Publisher | : World Scientific |
| Total Pages | : 331 |
| Release | : 2020-09-03 |
| Genre | : Mathematics |
| ISBN | : 9811213488 |
Download Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic Book in PDF, ePub and Kindle
Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
| Author | : Peter Rowlands |
| Publisher | : World Scientific |
| Total Pages | : 738 |
| Release | : 2007 |
| Genre | : Science |
| ISBN | : 9812709142 |
Download Zero to Infinity Book in PDF, ePub and Kindle
Rowlands offers researchers in quantum, theoretical and high energy physics immediate access to simple but powerful techniques.
| Author | : |
| Publisher | : |
| Total Pages | : 732 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : |
Download Mathematical Reviews Book in PDF, ePub and Kindle
| Author | : Alexey Stakhov |
| Publisher | : World Scientific |
| Total Pages | : 244 |
| Release | : 2020-09-03 |
| Genre | : Mathematics |
| ISBN | : 9811213518 |
Download Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences Book in PDF, ePub and Kindle
Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
