Alexander Invariant

The Alexander invariant of a Knot is the Homology of theInfinite cyclic cover of the complement of , considered as a Module over , the Ring ofintegral Laurent Polynomials. The Alexander invariant for a classical Tame Knot isfinitely presentable, and only is significant.

For any Knot in whose complement hasthe homotopy type of a Finite Complex, the Alexander invariant is finitely generated and therefore finitelypresentable. Because the Alexander invariant of a Tame Knot in has a Squarepresentation Matrix, its Alexander Ideal is Principal and it has anAlexander Polynomial denoted .

References

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 206-207, 1976.

• Appell Hypergeometric Function
• Appell Polynomial
• Appell Transformation
• Apple
• Approximately Equal
• Approximation Theory
• Apéry's Constant
• Arakelov Theory
• Arbelos
• Arborescence
• Arboricity
• Arc
• Arch
• Archimedean Solid
• Archimedean Solid Stellation
• Archimedean Spiral
• Archimedean Spiral Inverse Curve
• Archimedean Valuation
• Archimedes Algorithm
• Archimedes' Axiom
• Archimedes' Cattle Problem
• Archimedes' Circles
• Archimedes' Constant
• Archimedes' Hat-Box Theorem
• Archimedes' Lemma