Quandles and Topological Pairs

Symmetry, Knots, and Cohomology

Nonfiction, Science & Nature, Mathematics, Topology, Algebra
Cover of the book Quandles and Topological Pairs by Takefumi Nosaka, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Takefumi Nosaka ISBN: 9789811067938
Publisher: Springer Singapore Publication: November 20, 2017
Imprint: Springer Language: English
Author: Takefumi Nosaka
ISBN: 9789811067938
Publisher: Springer Singapore
Publication: November 20, 2017
Imprint: Springer
Language: English

This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles.

More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology.

For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some “relative homology”. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles.

The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles.

More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology.

For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some “relative homology”. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles.

The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.

More books from Springer Singapore

Cover of the book Renewable Energy Integration by Takefumi Nosaka
Cover of the book Thorium—Energy for the Future by Takefumi Nosaka
Cover of the book Quest for World-Class Teacher Education? by Takefumi Nosaka
Cover of the book Shaping the University of the Future by Takefumi Nosaka
Cover of the book China-Japan Relations in the 21st Century by Takefumi Nosaka
Cover of the book Futuristic Composites by Takefumi Nosaka
Cover of the book Data Science by Takefumi Nosaka
Cover of the book Attitudinal Evaluation in Chinese University Students’ English Writing by Takefumi Nosaka
Cover of the book Corporal Punishment in Rural Schools by Takefumi Nosaka
Cover of the book Green Symbiotic Cloud Communications by Takefumi Nosaka
Cover of the book Geometry of Cauchy-Riemann Submanifolds by Takefumi Nosaka
Cover of the book Enterprise Risk Management in International Construction Operations by Takefumi Nosaka
Cover of the book Researching and Teaching Second Language Speech Acts in the Chinese Context by Takefumi Nosaka
Cover of the book Digital Signal Processing with Matlab Examples, Volume 1 by Takefumi Nosaka
Cover of the book Preeclampsia by Takefumi Nosaka
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy