Title: Quandles : an introduction to the algebra of knots /
Authors: Elhamdadi, Mohamed, 1968-; Nelson, Sam, 1974-
Year: 2015
Subjects: Manifolds and cell complexes -- PL-topology -- Knots and links (in high dimensions); Group theory and generalizations -- Other generalizations of groups -- Sets with a single binary operation (groupoids); Knot theory.; Low-dimensional topology.; Manifolds and cell complexes -- Low-dimensional topology -- Knots and links in $S^3$.; Algebraic topology -- Classical topics -- Degree, winding number.; Group theory and generalizations -- Other generalizations of groups -- Loops, quasigroups.; Group theory and generalizations -- Permutation groups -- General theory for finite groups.; Algebraic topology -- Homology and cohomology theories -- Other homology theories.; Manifolds and cell complexes -- Low-dimensional topology -- Fundamental group, presentations, free differential calculus.; Manifolds and cell complexes -- Low-dimensional topology -- Invariants of knots and 3-manifolds.; Knot theory; Low-dimensional topology
Abstract: Quandles and their kin--kei racks, biquandles, and biracks--are algebraic structures whose axioms encode the movement of knots in space, say Elhamdadi and Nelson, in the same way that groups encode symmetry and orthogonal transformations encode rigid motion. They introduce quandle theory to readers who are comfortable with linear algebra and basic set theory but may have no previous exposure to abstract algebra, knot theory, or topology. They cover knots and links, quandles, quandles and groups, generalizations of quandles, enhancements, and generalized knots and links.
Contents: Knots and links -- Algebraic structures -- Quandles -- Quandles and groups -- Generalizations of quandles -- Enhancements -- Generalized knots and links.