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.
- Form
- Formal Logic
- Form (Geometric)
- Formosa Theorem
- Form (Polynomial)
- Formula
- Fortunate Prime
- Forward Difference
- Fountain
- Four Coins Problem
- Four-Color Theorem
- Fourier-Bessel Series
- Fourier-Bessel Transform
- Fourier Cosine Series
- Fourier Cosine Transform
- Fourier Integral
- Fourier Matrix
- Fourier-Mellin Integral
- Fourier Series
- Fourier Series--Power Series
- Fourier Series--Right Triangle
- Fourier Series--Square Wave
- Fourier Series--Triangle
- Fourier Series--Triangle Wave
- Fourier Sine Series