Masahico Saito's Books

Surfaces in 4-Space

By: Scott Carter,Seiichi Kamada,Masahico Saito

Write a review Read reviews Take a Quiz Solve Book Puzzle

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

220

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662101629

ISBN 13

9783662101629

The Classical and Quantum 6j-symbols. (MN-43), Volume 43

By: J. Scott Carter,Daniel E. Flath,Masahico Saito

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Classical and Quantum 6j-symbols. (MN-43), Volume 43

By: J. Scott Carter,Daniel E. Flath,Masahico Saito

Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals. The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Ub-3.0 qb0(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

178

Publisher

Princeton University Press

Published Date

ISBN 10

0691234671

ISBN 13

9780691234670

Knotted Surfaces and Their Diagrams

By: J. Scott Carter,Masahico Saito

Write a review Read reviews Take a Quiz Solve Book Puzzle

Knotted Surfaces and Their Diagrams

By: J. Scott Carter,Masahico Saito

In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts. The authors show how to unknot intricate examples using these moves. The third chapter reviews the braid theory of knotted surfaces. Examples of the Alexander isotopy are given, and the braid movie moves are presented. In the fourth chapter, properties of the projections of knotted surfaces are studied. Oriented surfaces in 4-space are shown to have planar projections without cusps and without branch points. Signs of triple points are studied. Applications of triple-point smoothing that include proofs of triple-point formulas and a proof of Whitney's congruence on normal Euler classes are presented. The fifth chapter indicates how to obtain presentations for the fundamental group and the Alexander modules. Key examples are worked in detail. The Seifert algorithm for knotted surfaces is presented and exemplified. The sixth chapter relates knotted surfaces and diagrammatic techniques to 2-categories. Solutions to the Zamolodchikov equations that are diagrammatically obtained are presented. The book contains over 200 illustrations that illuminate the text. Examples are worked out in detail, and readers have the opportunity to learn first-hand a series of remarkable geometric techniques.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

273

Publisher

American Mathematical Society

Published Date

ISBN 10

1470476339

ISBN 13

9781470476335

Surfaces in 4-Space

By: Scott Carter,Seiichi Kamada,Masahico Saito

Write a review Read reviews Take a Quiz Solve Book Puzzle

Surfaces in 4-Space

By: Scott Carter,Seiichi Kamada,Masahico Saito

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

220

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662101629

ISBN 13

9783662101629

Knotted Surfaces and Their Diagrams

By: J. Scott Carter,Masahico Saito

Write a review Read reviews Take a Quiz Solve Book Puzzle

Knotted Surfaces and Their Diagrams

By: J. Scott Carter,Masahico Saito

In this text, the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in three-dimensional space. Knotted surface diagrams are defined; the theory of Reidemeister moves is developed; and the braid theory of knotted surfaces is

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

273

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821805932

ISBN 13

9780821805930

The Classical and Quantum 6j-symbols

By: J. Scott Carter,Daniel E. Flath,Masahico Saito

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Classical and Quantum 6j-symbols

By: J. Scott Carter,Daniel E. Flath,Masahico Saito

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

178

Publisher

Princeton University Press

Published Date

ISBN 10

0691027307

ISBN 13

9780691027302

Book's by Masahico Saito

Surfaces in 4-Space

Surfaces in 4-Space

The Classical and Quantum 6j-symbols. (MN-43), Volume 43

The Classical and Quantum 6j-symbols. (MN-43), Volume 43

Knotted Surfaces and Their Diagrams

Knotted Surfaces and Their Diagrams

Surfaces in 4-Space

Surfaces in 4-Space

Knotted Surfaces and Their Diagrams

Knotted Surfaces and Their Diagrams

The Classical and Quantum 6j-symbols

The Classical and Quantum 6j-symbols

Username

Password

Username

Password

Password again

Birthday

Email