Frequently Asked Questions


The Enter a knot page lets you enter a knot by name, for instance "4_1" or 11a_123", and returns all the invariants for that particular knot. A diagram of the knot is available by clicking on the small image of the knot.

The Advanced Search page has a special search function that gives all the knots with a specific value or range of values for a specific invariant.

If an invariant value is formatted as a word or polynomial expression, in the advanced search page it must be typed exactly as it appears in the table. It could be easiest to copy a known value from a table and paste it into the search box. The website creators are currently working to make the search function recognize less exact entries.

Checking the second box under the Advanced Search text-entry box will include knots with unknown values of an invariant in the results. To search for knots with unknown values, enter a question mark "?" in the search box and be sure to check the box asking "result includes knots with unknown value.'' Some invariant values are not known exactly but are known to be within a certain range. These are written as an interval. For example, [1, 3] means the the possible values are either 1, 2, or 3.


The invariants are grouped into categories based on the type of information they give about knots.

To learn how an invariant works and how to calculate it, click on its name on the homepage. Many of these descriptive page give background information and references.

The results page can be sorted by each column by clicking on the column header. Repeat clicks toggle between ascending and descending order. Blank entries appear last in both ascending and descending order. The simple "[" is larger than any numeric entry. Non-numerical entries are sorted lexicographically.

To perform more sophisticated sorting, click the "Export to CSV" button on the results page to download the table as a .csv file and open it as a spreadsheet.

For some knots and invariants, the exact value is unknown but within a certain definite range. Square brackets denote these ranges of possible values. Curly brackets are used when an invariant is a set of multiple values.

The invariants listed on this website do not depend on a knot's orientation, but the PD notation for a knot does change if you change its orientation (or take its mirror image). Reconstructing a knot from its PD notation gives it an orientation. For a further discussion visit the Orientation page.

The description pages for many invariants include references and values for specific knots.

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Some of the description pages invariants provide references for the computation of the invariant value for particular knots. On the results page, values of invariants for which there are specific references appear underlined and are linked to the descriptive page.

Some excellent references include the following: (Adams, Livingston, Rolfsen, Burde-Zieschang).


Some sources include: KnotAtlas .....

Some sources include: Snappy, Szabo HF calculator, ...