The Jones polynomial is an algebraic fingerprint for knots. Resolve crossings to compute it step by step.
Step: Select a knot
Choose a knot above, then resolve crossings in the diagram. At each crossing, choose to smooth it vertically (0-resolution) or horizontally (infinity-resolution).
Jones Polynomial V(t):
Select a knot to begin
Resolution tree: 0 nodes
Bracket Polynomial: <K> = A<K₀> + A⁻¹<K∞>
Each simple loop contributes: (-A² - A⁻²)
The Jones polynomial is a knot INVARIANT: different diagrams of the same knot give the same polynomial.