Algebraic Knot Theory
Algebraic knot theory uses algebraic structures like groups and polynomials to classify knots, which are closed loops embedded in 3D space. Knot invariants such as the knot group, Alexander polynomial, and Jones polynomial are algebraic objects that remain unchanged under continuous deformations, allowing us to distinguish different knots by examining their algebraic properties.
"Note 1: Introduction to Knot Theory and its Algebraic Roots: Knot theory, a branch of topology, studies mathematical knots. Unlike everyday knots, mathematical knots are closed loops, meanin...