Manifolds and cell complexes Knot theory Concept
Knot invariant
Summary
A knot invariant is a quantity attached to each knot that takes the same value on equivalent knots. Invariants are the main tool to prove that two knots are different: if an invariant differs, the knots are not equivalent. Examples are the crossing number, the knot group, tricolorability, the Alexander polynomial and the Jones polynomial.
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About this page
| Tag | GZQ5ZE3X6G |
|---|---|
| URI | m2://GZQ5ZE3X6G |
| Kind | concept |
| Writing | W0 stub |
| MSC | 57K10, 57K14 |
| Same as | |
| Changed | 2 November 2026 |
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Special cases
- Jones polynomial
- Knot Floer homology
- Kontsevich integral
- Bridge number
- Alexander polynomial
- Unknotting number
- HOMFLY polynomial
- Finite type invariant
- Khovanov homology