: Mathematics: knot theory

topology > algebraic topology > knot theory

knot theory

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, ${\\displaystyle \\mathbb {R} ^{3}}$ . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of ${\\displaystyle \\mathbb {R} ^{3}}$ upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Knot_theory)

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