Seeing Four Dimensional Space And Beyond Using Knots

Download Seeing Four Dimensional Space And Beyond Using Knots full books in PDF, epub, and Kindle. Read online free Seeing Four Dimensional Space And Beyond Using Knots ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Seeing Four-dimensional Space And Beyond: Using Knots!

Seeing Four-dimensional Space And Beyond: Using Knots!
Author :
Publisher : World Scientific
Total Pages : 173
Release :
ISBN-10 : 9789811275166
ISBN-13 : 9811275165
Rating : 4/5 (165 Downloads)

Book Synopsis Seeing Four-dimensional Space And Beyond: Using Knots! by : Eiji Ogasa

Download or read book Seeing Four-dimensional Space And Beyond: Using Knots! written by Eiji Ogasa and published by World Scientific. This book was released on 2023-07-21 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Seeing Four-dimensional Space And Beyond: Using Knots! Related Books

Seeing Four-dimensional Space And Beyond: Using Knots!
Language: en
Pages: 173
Authors: Eiji Ogasa
Categories: Mathematics
Type: BOOK - Published: 2023-07-21 - Publisher: World Scientific

DOWNLOAD EBOOK

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 beginn
Quipu: Decorated Permutation Representations Of Finite Groups
Language: en
Pages: 456
Authors: Yongju Bae
Categories: Mathematics
Type: BOOK - Published: 2024-06-27 - Publisher: World Scientific

DOWNLOAD EBOOK

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 le
Scientific Legacy Of Professor Zbigniew Oziewicz: Selected Papers From The International Conference
Language: en
Pages: 771
Authors: Hilda Maria Colin Garcia
Categories: Mathematics
Type: BOOK - Published: 2023-09-27 - Publisher: World Scientific

DOWNLOAD EBOOK

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
The Knot Book
Language: en
Pages: 330
Authors: Colin Conrad Adams
Categories: Mathematics
Type: BOOK - Published: 2004 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

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 thi
High-dimensional Knot Theory
Language: en
Pages: 669
Authors: Andrew Ranicki
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the