Seeing Four Dimensional Space And Beyond Using Knots
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Seeing Four Dimensional Space And Beyond
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Author : Eiji Ogasa
language : en
Publisher:
Release Date : 2023
Seeing Four Dimensional Space And Beyond written by Eiji Ogasa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Four-manifolds (Topology) categories.
"An introductory text for knot theory. Introduces the tool for visualizing 4- and higher-dimensional space. Also discusses recent developments in the field"--
Seeing Four Dimensional Space And Beyond Using Knots
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Author : Eiji Ogasa
language : en
Publisher: World Scientific
Release Date : 2023-07-21
Seeing Four Dimensional Space And Beyond Using Knots written by Eiji Ogasa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-21 with Mathematics categories.
According to string theory, our universe exists in a 10- or 11-dimensional space. However, the idea the space beyond 3 dimensions seems hard to grasp for beginners. This book presents a way to understand four-dimensional space and beyond: with knots! Beginners can see high dimensional space although they have not seen it.With visual illustrations, we present the manipulation of figures in high dimensional space, examples of which are high dimensional knots and n-spheres embedded in the (n+2)-sphere, and generalize results on relations between local moves and knot invariants into high dimensional space.Local moves on knots, circles embedded in the 3-space, are very important to research in knot theory. It is well known that crossing changes are connected with the Alexander polynomial, the Jones polynomial, HOMFLYPT polynomial, Khovanov homology, Floer homology, Khovanov homotopy type, etc. We show several results on relations between local moves on high dimensional knots and their invariants.The following related topics are also introduced: projections of knots, knot products, slice knots and slice links, an open question: can the Jones polynomial be defined for links in all 3-manifolds? and Khovanov-Lipshitz-Sarkar stable homotopy type. Slice knots exist in the 3-space but are much related to the 4-dimensional space. The slice problem is connected with many exciting topics: Khovanov homology, Khovanv-Lipshits-Sarkar stable homotopy type, gauge theory, Floer homology, etc. Among them, the Khovanov-Lipshitz-Sarkar stable homotopy type is one of the exciting new areas; it is defined for links in the 3-sphere, but it is a high dimensional CW complex in general.Much of the book will be accessible to freshmen and sophomores with some basic knowledge of topology.
Four Dimensional Paper Constructions After Mobius Klein And Boy
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Author : Eiji Ogasa
language : en
Publisher: World Scientific
Release Date : 2025-03-05
Four Dimensional Paper Constructions After Mobius Klein And Boy written by Eiji Ogasa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-05 with Mathematics categories.
Explore four-dimensional paper constructions inspired by the work of great mathematicians like Möbius, Klein, Boy, Hopf, and others. These creations will help you visualize four-dimensional space and beyond, transporting you to higher-dimensional spaces. This book is designed to solidify your foundations in various areas of mathematics and physics, with a particular focus on topology.If you are familiar with higher-dimensional spaces from loving sci-fi stories, you may find the four-dimensional illustrations in this book especially intuitive. Imagine starting on Earth and traveling straight up into the universe — where would you end up? Perhaps you would travel in one direction only to eventually return to your starting point. Can you imagine what happens during the course of this trip? By engaging with these four-dimensional paper constructions, you will gain a deeper understanding of this fascinating journey.
Combinatorial Knot Theory
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Author : Roger A Fenn
language : en
Publisher: World Scientific
Release Date : 2024-11-27
Combinatorial Knot Theory written by Roger A Fenn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-27 with Mathematics categories.
A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent planar graph or network in the horizontal plane, with the vertices or crossings corresponding to double points of a projection. At this stage we have the shadow of the knot defined by the projection. We can reconstruct the knot by lifting the crossings into two points in space, one above the other. This information is preserved at the vertices by cutting the arc which appears to go under the over crossing arc. We can then act on this diagram of the knot using the famous Reidemeister moves to mimic the motion of the knot in space. The result is classic combinatorial knot theory. In recent years, many different types of knot theories have been considered where the information stored at the crossings determines how the Reidemeister moves are used, if at all.In this book, we look at all these new theories systematically in a way which any third-year undergraduate mathematics student would understand. This book can form the basis of an undergraduate course or as an entry point for a postgraduate studying topology.
Quipu Decorated Permutation Representations Of Finite Groups
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Author : Yongju Bae
language : en
Publisher: World Scientific
Release Date : 2024-06-27
Quipu Decorated Permutation Representations Of Finite Groups written by Yongju Bae and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-27 with Mathematics categories.
This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.
Scientific Legacy Of Professor Zbigniew Oziewicz Selected Papers From The International Conference Applied Category Theory Graph Operad Logic
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Author : Hilda Maria Colin Garcia
language : en
Publisher: World Scientific
Release Date : 2023-09-27
Scientific Legacy Of Professor Zbigniew Oziewicz Selected Papers From The International Conference Applied Category Theory Graph Operad Logic written by Hilda Maria Colin Garcia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.
Dedicated to the memory of the late Professor Zbigniew Oziewicz from Universidad Nacional Autónoma de México, the book consists of papers on a wide variety of topics related to the work of Professor Oziewicz, which were presented at the special conference on Graph-Operads-Logic (GOL 2021), selected through peer review to promote his scientific legacy.Professor Oziewicz was a great enthusiast and supporter of category theory and its applications in physics, as well as in various areas of mathematics (topology, noncommutative geometry, etc.). In particular, he made significant contributions to the theory of Frobenius algebras, which now are becoming more important due to their connection with topological quantum field theories that are used in mathematical physics and in quantum topology. Professor Oziewicz was a great and very generous teacher, who immersed his students in the beautiful ideas of category theory as well as mathematical physics and computation. It was his idea to start a series of conferences under the title Graphs-Operads-Logic, most of them held in Mexico, with some of them in the USA, which were a great platform to discuss various ideas connected with category theory and its various applications, and to make friends with other scientists. Despite his passing, the GOL 2021 conference is included in this series to pay tribute to his many contributions to diverse areas of science.The book is laid out in twelve main topics where we can find relevant works from distinguished experts.
Beyond Perception
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Author : Chuck Missler
language : en
Publisher: Koinonia House
Release Date : 2023-01-19
Beyond Perception written by Chuck Missler and has been published by Koinonia House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-19 with Religion categories.
Why do scientists now believe we live in a 10-dimensional universe? Has physics finally reached the very boundaries of reality? There seems to be evidence to suggest that our world and everything in it are only ghostly images: projections from a level of reality so beyond our own that the real reality is literally beyond both space and time. The main architect of this astonishing idea is one of the world's most eminent thinkers- physicist David Bohm, a protege of Einstein's. Earlier, he noticed that, in plasmas, particles stopped behaving like individuals and started behaving as if they were part of a larger and inter connected whole. He continued his work in the behavior of oceans of these particles, noting their behaving as if they know what each on the untold trillions of individual particles were doing.
The Poetry Of Victorian Scientists
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Author : Daniel Brown
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
The Poetry Of Victorian Scientists written by Daniel Brown and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Literary Criticism categories.
The first study of poetry by Victorian scientists, a unique record of the nature and cultures of Victorian science.
English Mechanic And Mirror Of Science And Art
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Author :
language : en
Publisher:
Release Date : 1883
English Mechanic And Mirror Of Science And Art written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1883 with Technology categories.
Intelligence Of Low Dimensional Topology 2006
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Author : J Scott Carter
language : en
Publisher: World Scientific
Release Date : 2007-05-29
Intelligence Of Low Dimensional Topology 2006 written by J Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-29 with Mathematics categories.
This volume gathers the contributions from the international conference “Intelligence of Low Dimensional Topology 2006,” which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.