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.

• Partition
• Partition Function P
• Partition Function Q
• Part Metric
• Party Problem
• Parzen Apodization Function
• Pascal Distribution
• Pascal Line
• Pascal's Formula
• Pascal's Hexagrammum Mysticum
• Pascal's Limaçon
• Pascal's Rule
• Pascal's Theorem
• Pascal's Triangle
• Pascal's Wager
• Pasch's Axiom
• Pasch's Theorem
• Pass Equivalent
• Pass Move
• Patch
• Path
• Path Graph
• Path Integral
• Pathwise-Connected
• Patriarchal Cross