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The determinant of a knot is defined as |Delta(-1)|, where Delta(z) is the Alexander polynomial (Rolfsen 1976, p. 213).

A relationship between knot polynomials for links in different orientations (denoted below as L_+, L_0, and L_-). J. H. Conway was the first to realize that the Alexander ...

The graph sum of graphs G and H is the graph with adjacency matrix given by the sum of adjacency matrices of G and H. A graph sum is defined when the orders of G and H are ...

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

The arf invariant is a link invariant that always has the value 0 or 1. A knot has Arf invariant 0 if the knot is "pass equivalent" to the unknot and 1 if it is pass ...

Construct a chain C of 2n components in a solid torus V. Now thicken each component of C slightly to form a chain C_1 of 2n solid tori in V, where pi_1(V-C_1)=pi_1(V-C) via ...

Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space. Cohomology has more algebraic structure than homology, ...

The Kinoshita-Terasaka knot is the prime knot on eleven crossings with braid word ...

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...

The Miller Institute knot is the 6-crossing prime knot 6_2. It is alternating, chiral, and invertible. A knot diagram of its laevo form is illustrated above, which is ...