Table of Knot Invariants

*Please Cite KnotInfo* Knot Atlas Knot Theory Links
Knot Theory Calculators Unknown Values (last updated: 16 May 2008) Acknowledgments

Build a Knot Table. Welcome to KnotInfo. Check the desired boxes in the sections below and then click SUBMIT on the page to produce your desired table of knots. If you do not know the name of a particular knot you are interested in, KnotFinder can help you.

New advanced search feature is now available! [Advanced Search]

 Select knots you want tabulated. [Advanced Search]
Specify crossing numbers. The letters a and n designate alternating and nonalternating knots. 12 crossing knots are grouped.
3-6 7 8 9 10
11a 11n 12a (1-200) 12a (201-400) 12a (401-600)
12a (601-800) 12a (801-1000) 12a (1001-1200) 12a (1200-1288) 12n (1-200)
12n (201-400) 12n (401-600) 12n (601-800) 12n (801-888) All

 Names and descriptions. Please select the naming and notational descriptions desired. Names are linked to diagrams.
Name Name Rank Alternating DT Name
DT Notation DT Rank Classical Conway Name Conway Notation
Gauss Notation PD Notation Braid Notation Two-Bridge Notation
Fibered Tetrahedral Census Name

 Three-Dimensional Invariants.
Arc Index Braid Index Braid Length Bridge Index
Crossing Number Determinant Nakanishi Index Polygon Index
Seifert Matrix Super Bridge Index Symmetry Type Three Genus
Crosscap Number Thurston-Bennequin Number Morse-Novikov Number Tunnel Number
Turaev Genus Unknotting Number

 Concordance and Four-Dimensional Invariants.
Arf Invariant Smooth Concordance Genus Topological Concordance Genus Smooth Concordance Order
Topological Concordance Order Algebraic Concordance Order Smooth Four Genus Topological Four Genus
Smooth 4D Crosscap Number Topological 4D Crosscap Number Rasmussen Invariant Ozsvath-Szabo Tau-Invariant
Signature Smooth Concordance Crosscap Number Topological Concordance Crosscap Number

 Polynomial Invariants.
A-Polynomial Alexander Polynomial Conway Polynomial HOMFLY Polynomial
Jones Polynomial Kauffman Polynomial Khovanov Polynomial Khovanov Torsion Polynomial

 Hyperbolic Invariants.
Volume Maximum Cusp Volume Longitude Length Meridian Length
Longitude Translation Meridian Translation Other Short Geodesics Full Symmetry Group
Chern-Simons Invariant

 Diagrams and Other Information. Check if you want to see small diagrams (linked to larger figures) and if you want the the table to include links to the Knot Atlas site.
Diagram Knot Atlas Page

 Submission. Click to submit query.


KnotInfo was created and is maintained by Chuck Livingston with the assistance of Jae Choon Cha. Please send your comments to Chuck Livingston: livingst@indiana.edu. Knotinfo is partially supported by Indiana University and by the NSF.

Charles Livingston
Department of Mathematics
Indiana University
Bloomington, IN 47405, U.S.A.
Jae Choon Cha
Department of Mathematics
POSTECH
Pohang Gyungbuk 790-784, Republic of Korea