@article{805877,
      recid = {805877},
      author = {Nosaka, Takefumi,},
      title = {Quandles and topological pairs : symmetry, knots, and  cohomology /},
      publisher = {Springer,},
      address = {Sinagpore :},
      pages = {1 online resource.},
      year = {2017},
      abstract = {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.--},
      url = {http://library.usi.edu/record/805877},
}