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.

• Augmented Triangular Prism
• Augmented Tridiminished Icosahedron
• Augmented Truncated Cube
• Augmented Truncated Dodecahedron
• Augmented Truncated Tetrahedron
• Aureum Theorema
• Aurifeuillean Factorization
• Ausdehnungslehre
• Authalic Latitude
• Autocorrelation
• Automorphic Function
• Automorphic Number
• Automorphism
• Automorphism Group
• Autonomous
• Autoregressive Model
• Auxiliary Circle
• Auxiliary Latitude
• Auxiliary Triangle
• Average
• Average Absolute Deviation
• Average Function
• Average Seek Time
• Semisecant
• Semisimple