Table of Knot Invariants

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Specify crossing numbers. The letters a and n designate alternating and nonalternating knots. 12 crossing knots are grouped.
3-678910
11a11n12a (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 Monodromy Tetrahedral Census Name
Three-Dimensional Invariants.
Arc Index Braid Index Braid Length Bridge Index
Crosscap Number Crossing Number Determinant Morse-Novikov Number
Nakanishi Index Polygon Index Seifert Matrix Small or Large
Super Bridge Index Symmetry Type Three Genus Thurston-Bennequin Number
Tunnel Number Turaev Genus Unknotting Number Width
Concordance and Four-Dimensional Invariants.
Arf Invariant Four-Ball Crossing Number 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 Signature Function Smooth Concordance Crosscap Number
Topological Concordance Crosscap Number
Positivity.
Positive Braid Positive Strongly Quasipositive Quasipositive
Positive Braid Notation Positive PD notation Strongly Quasipositive Braid Notation Quasipositive Braid Notation
Polynomial Invariants.
A-Polynomial Alexander Polynomial Conway Polynomial HOMFLY Polynomial
Jones Polynomial Kauffman Polynomial Khovanov Polynomial Khovanov Torsion Polynomial
Show polynomials as coefficient vectors
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 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. Privacy Notice

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