Quandles

Description:

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.

subjects: Group theory and generalizations -- Other generalizations of groups -- Loops, quasigroups,  Knot theory,  Algebraic topology -- Classical topics -- Degree, winding number,  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),  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,  Manifolds and cell complexes -- Low-dimensional topology -- Knots and links in $S^3$,  Algebraic topology -- Homology and cohomology theories -- Other homology theories,  Group theory and generalizations -- Permutation groups -- General theory for finite groups,  Low-dimensional topology,  Topology