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Quandles and Topological Pairs - Symmetry, Knots, and Cohomology (Paperback, 1st ed. 2017)
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Quandles and Topological Pairs - Symmetry, Knots, and Cohomology (Paperback, 1st ed. 2017)
Series: SpringerBriefs in Mathematics
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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.
General
Imprint: |
Springer Verlag, Singapore
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Country of origin: |
Singapore |
Series: |
SpringerBriefs in Mathematics |
Release date: |
November 2017 |
First published: |
2017 |
Authors: |
Takefumi Nosaka
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Dimensions: |
235 x 155mm (L x W) |
Format: |
Paperback
|
Pages: |
136 |
Edition: |
1st ed. 2017 |
ISBN-13: |
978-981-10-6792-1 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
General
|
LSN: |
981-10-6792-9 |
Barcode: |
9789811067921 |
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