000805877 000__ 03422cam\a2200445K\\4500
000805877 001__ 805877
000805877 005__ 20230306143811.0
000805877 006__ m\\\\\o\\d\\\\\\\\
000805877 007__ cr\un\nnnunnun
000805877 008__ 171128s2017\\\\si\\\\\\o\\\\\000\0\eng\d
000805877 019__ $$a1012939328$$a1013523136
000805877 020__ $$a9789811067938$$q(electronic book)
000805877 020__ $$a9811067937$$q(electronic book)
000805877 020__ $$z9789811067921
000805877 020__ $$z9811067929
000805877 035__ $$aSP(OCoLC)on1013174825
000805877 035__ $$aSP(OCoLC)1013174825$$z(OCoLC)1012939328$$z(OCoLC)1013523136
000805877 040__ $$aYDX$$beng$$cYDX$$dN$T$$dEBLCP$$dGW5XE$$dFIE
000805877 049__ $$aISEA
000805877 050_4 $$aQA612.2
000805877 08204 $$a514/.2242$$223
000805877 1001_ $$aNosaka, Takefumi,$$eauthor.
000805877 24510 $$aQuandles and topological pairs :$$bsymmetry, knots, and cohomology /$$cTakefumi Nosaka.
000805877 260__ $$aSinagpore :$$bSpringer,$$c2017.
000805877 300__ $$a1 online resource.
000805877 336__ $$atext$$btxt$$2rdacontent
000805877 337__ $$acomputer$$bc$$2rdamedia
000805877 338__ $$aonline resource$$bcr$$2rdacarrier
000805877 4901_ $$aSpringer briefs in mathematics
000805877 506__ $$aAccess limited to authorized users.
000805877 520__ $$aThis 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.--$$cProvided by publisher.
000805877 588__ $$aOnline resource; title from PDF title page (viewed November 30, 2017).
000805877 650_0 $$aKnot theory.
000805877 650_0 $$aLow-dimensional topology.
000805877 77608 $$iPrint version:$$z9811067929$$z9789811067921$$w(OCoLC)1004042979
000805877 830_0 $$aSpringerBriefs in mathematics.
000805877 852__ $$bebk
000805877 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-981-10-6793-8$$zOnline Access$$91397441.1
000805877 909CO $$ooai:library.usi.edu:805877$$pGLOBAL_SET
000805877 980__ $$aEBOOK
000805877 980__ $$aBIB
000805877 982__ $$aEbook
000805877 983__ $$aOnline
000805877 994__ $$a92$$bISE