Seiichi Kamada's Books

Surfaces in 4-Space

By: Scott Carter,Seiichi Kamada,Masahico Saito

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Surfaces in 4-Space

By: Scott Carter,Seiichi Kamada,Masahico Saito

Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.

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Page Count

220

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662101629

ISBN 13

9783662101629

Braid and Knot Theory in Dimension Four

By: Seiichi Kamada

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Braid and Knot Theory in Dimension Four

By: Seiichi Kamada

Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa. In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it tostudy surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given. This book is the first to contain a complete proof of the generalized Markov theorem. Surface links are studied via the motion picture method, and some important techniques of this method arestudied. For surface braids, various methods to describe them are introduced and developed: the motion picture method, the chart description, the braid monodromy, and the braid system. These tools are fundamental to understanding and computing invariants of surface braids and surface links. Included is a table of knotted surfaces with a computation of Alexander polynomials. Braid techniques are extended to represent link homotopy classes. The book is geared toward a wide audience, from graduatestudents to specialists. It would make a suitable text for a graduate course and a valuable resource for researchers.

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Page Count

329

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829696

ISBN 13

9780821829691

Surface-Knots in 4-Space

An Introduction

By: Seiichi Kamada

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Surface-Knots in 4-Space

An Introduction

By: Seiichi Kamada

This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.

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Page Count

215

Publisher

Springer

Published Date

ISBN 10

9811040915

ISBN 13

9789811040917

Diagrammatic Algebra

By: J. Scott Carter,Seiichi Kamada

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Diagrammatic Algebra

By: J. Scott Carter,Seiichi Kamada

This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.

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Page Count

365

Publisher

American Mathematical Society

Published Date

ISBN 10

1470466716

ISBN 13

9781470466718

Moving Particle Semi-implicit Method

A Meshfree Particle Method for Fluid Dynamics

By: Seiichi Koshizuka,Kazuya Shibata,Masahiro Kondo,Takuya Matsunaga

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Moving Particle Semi-implicit Method

A Meshfree Particle Method for Fluid Dynamics

By: Seiichi Koshizuka,Kazuya Shibata,Masahiro Kondo,Takuya Matsunaga

Moving Particle Semi-implicit Method: A Meshfree Particle Method for Fluid Dynamics begins by familiarizing the reader with basic theory that supports their journey through sections on advanced MPH methods. The unique insights that this method provides include fluid-structure interaction, non-Newtonian flow, and cavitation, making it relevant to a wide range of applications in the mechanical, structural, and nuclear industries, and in bioengineering. Co-authored by the originator of the MPS method, this book is the most authoritative guide available. It will be of great value to students, academics and researchers in industry. - Presents the differences between MPH and SPH, helping readers choose between methods for different purposes - Provides pieces of computer code that readers can use in their own simulations - Includes the full, extended algorithms - Explores the use of MPS in a range of industries and applications, including practical advice

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Page Count

307

Publisher

Academic Press

Published Date

ISBN 10

0128128372

ISBN 13

9780128128374

Surfaces in 4-Space

By: Scott Carter,Seiichi Kamada,Masahico Saito

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Surfaces in 4-Space

By: Scott Carter,Seiichi Kamada,Masahico Saito

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Page Count

220

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662101629

ISBN 13

9783662101629

Surface-Knots in 4-Space

An Introduction

By: Seiichi Kamada

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Surface-Knots in 4-Space

An Introduction

By: Seiichi Kamada

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Solve jigsaw puzzle

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Page Count

215

Publisher

Springer

Published Date

ISBN 10

9811040915

ISBN 13

9789811040917

Braid and Knot Theory in Dimension Four

By: Seiichi Kamada

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Braid and Knot Theory in Dimension Four

By: Seiichi Kamada

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N/A

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Solve jigsaw puzzle

Age

Page Count

329

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829696

ISBN 13

9780821829691

Book's by Seiichi Kamada

Surfaces in 4-Space

Surfaces in 4-Space

Braid and Knot Theory in Dimension Four

Braid and Knot Theory in Dimension Four

Surface-Knots in 4-Space

Surface-Knots in 4-Space

Diagrammatic Algebra

Diagrammatic Algebra

Moving Particle Semi-implicit Method

Moving Particle Semi-implicit Method

Surfaces in 4-Space

Surfaces in 4-Space

Surface-Knots in 4-Space

Surface-Knots in 4-Space

Braid and Knot Theory in Dimension Four

Braid and Knot Theory in Dimension Four

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