東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Quandles and topological pairs = sym...

Nosaka, Takefumi.

FindBook

Google Book

Amazon

博客來

Quandles and topological pairs = symmetry, knots, and cohomology /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quandles and topological pairs/ by Takefumi Nosaka.
其他題名:	symmetry, knots, and cohomology /
作者:	Nosaka, Takefumi.
出版者:	Singapore :Springer Singapore : : 2017.,
面頁冊數:	ix, 136 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Knot theory. -
電子資源:	http://dx.doi.org/10.1007/978-981-10-6793-8
ISBN:	9789811067938

Quandles and topological pairs = symmetry, knots, and cohomology /
Nosaka, Takefumi.

Quandles and topological pairssymmetry, knots, and cohomology /[electronic resource] :by Takefumi Nosaka. - Singapore :Springer Singapore :2017. - ix, 136 p. :ill., digital ;24 cm. - Springerbriefs in mathematics,2191-8198. - Springerbriefs in mathematics..

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.

ISBN: 9789811067938

Standard No.: 10.1007/978-981-10-6793-8doiSubjects--Topical Terms:

523755
Knot theory.

LC Class. No.: QA612.2

Dewey Class. No.: 514.2242

Quandles and topological pairs = symmetry, knots, and cohomology /
LDR:02813nmm a2200313 a 4500 001 2112560
003 DE-He213
005 20180522164232.0
006 m d
007 cr nn 008maaau
008 180719s2017 si s 0 eng d
020 $a 9789811067938 $q (electronic bk.)
020 $a 9789811067921 $q (paper)
024 7 $a 10.1007/978-981-10-6793-8 $2 doi
035 $a 978-981-10-6793-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612.2
072 7 $a PBP $2 bicssc
072 7 $a MAT038000 $2 bisacsh
082 0 4 $a 514.2242 $2 23
090 $a QA612.2 $b .N897 2017
100 1 $a Nosaka, Takefumi. $3 3270412
245 1 0 $a Quandles and topological pairs $h [electronic resource] : $b symmetry, knots, and cohomology / $c by Takefumi Nosaka.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2017.
300 $a ix, 136 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springerbriefs in mathematics, $x 2191-8198
520 $a 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.
650 0 $a Knot theory. $3 523755
650 0 $a Low-dimensional topology. $3 659140
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Topology. $3 522026
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a K-Theory. $3 897432
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Springerbriefs in mathematics. $3 3270340
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-6793-8
950 $a Mathematics and Statistics (Springer-11649)