About KnotInfo and LinkInfo

Welcome to the new KnotInfo and Linkinfo. We hope you like the new interface and the new features. These include the "Enter a knot" single knot search, new invariants and diagrams, and the option to easily download results as a csv file.

KnotInfo was created by Chuck Livingston in 2004. Soon after, Jae Choon Cha joined the project, helping to recode the site, adding many of its most popular features and creating Linkinfo. In 2019, Allison Moore began participating in the redesign and maintenance of KnotInfo. Eric Ost wrote most of the new code and did much of the preliminary design work. Please send your comments to Chuck or Allison, and please remember to cite KnotInfo if you use it. Knotinfo is partially supported by Indiana University and by the NSF.

Charles Livingston
Department of Mathematics
Indiana University
Bloomington, IN 47405, U.S.A.
Allison H. Moore
Department of Mathematics
Virginia Commonwealth Univerity
Richmond, VA 23284, U.S.A

KnotInfo Acknowledgments

Special thanks go to Dror Bar-Natan, Morwen Thistlethwaite, and Alexander Stoimenow for their assistance and advice. Much of the data was supplied by them, and they also caught many errors in our postings. Dror's excellent website Knot Atlas and programs there can be used to find more information and were the source of much of the data here. Morwen provide me with the files of knot diagrams. The program Knotscape, developed by Morwen and Jim Hoste, has also been put to great use. Knotscape uses SnapPea, a program written by Jeff Weeks, to compute hyperbolic invariants.

Sidharth Thakur created the original dynamic web pages used here, and graduate students of Indiana University did much of the work in building this website. The following graduate students of the Mathematics Department of Indiana University have participated in creating this site by computing knot invariants, writing web pages, and providing programing and other computer related assistance: Jennifer Franko, Tobias Hagge, Jiho Kim, Jason Lingle-martin, J.P. Nogami, Justin Pati, Noah Salvaterra, Cornelia Van Cott, and Jonathan Yazinski.

The computations of the 3-genus of 11 crossing knots was done by Jake Rasmussen, using the Ozsvath-Szabo knot Floer homology.

Thomas Gittings and Alexander Stoimenow provided me with valuable information about braids, included in the table. Alexander also caught many slip-ups in early versions of the table. Alexander verified the braid indices through twelve crossings and Thomas found the minimal length representatives (among all number of strands).

For the values of the unknotting numbers of 11 crossing knots, Slavik Jablan and Radmila Sazdanovic did the initial calculations, developing lower bounds based on the the nontriviality of the knots and the signature. Upper bounds were found using explicit calculations. More information can be found in Unknotting Number.

Peter Cromwell provided the data and write-up for the Arc Index of knots. The initial data for the Polygon Index of knots came from his book, "Knots and Links."

Dick Randell provided background information about the polygon number and also many new results concerning the super-bridge index.

Jim Hoste and Marc Culler provided a great deal of material regarding the A-polynomial. Abhijit Champanerkar helped write the descriptive information about the A-polynomial.

Slavik Jablan and Radmila Sazdanovic provided the site with a large variety of invariants. They have also made available their online knot theoretic calculators, LinKnot.

Kate Kearney edited many of the web pages, correcting errors, uniformizing the format of pages, and generally improving the expositiory content of the site.

Walter Neumann provided us wth the data for the complex volumes and Chern-Simons invariants of all hyperbolic knots with 12 or fewer crossings. He generated this using the program Snap.

Christoph Lamm has discovered several previously unknown ribbon knots among 11 crossing knots and has shared those with me. Alexander Stoimenow added to that list.

Radmila Sazdanovic provided me with the PD data for all 12 crossing knots. Using that, Adam Lowrance found estimates for the Turaev genus. I was also helped by David Futer in writing the intial description of the Turaev genus. Adam Lowrance has continued to provide me updates on the Turaev genus.

Rick Litherland performed extensive calculations of arc indices and Thursten-Bennequin numbers for 12-crossing knots.

Gyo Taek Jin provided us with results concerning the arc index, based on his joint work with Kim and Lee.

Lukas Lewark provided corrections to our data on Rasmussen invariants, correcting sign errors.

Carlo Angiuli rewrote large portions of the website, adding the preferences web page and also creating the mobile version of the site.

Benjamin Burton and Melih Ozlen provided us with results of their extended computations related to the crosscap number.

Thanks to Stefan Friedl and Maciej Borodzik for identifying many unkotting number 3 knots.

Mark C. Bell provided the initial data on monodromies of fibered knots.

Ben Burton has been particularly helpful with the data concerning crosscap numbers, the nonorientable 3--genus. Some of his work appears in Enumerating fundamental surfaces, Algorithms, experiments and invariants, preprint, arXiv:1111.7055v2

Brendan Owens and Saso Strle helped us with the addition of the clasp number to the list of 4-dimensional clasp number.

Ken Baker helped us with issues related to strongly quasipositive knots.

Kate Kearney made a number of significant contributions related to the concordance genus.

Joshua Howie caught significant errors in our tabulations of the Turaev invariant.

Thanks go to Colin Adams, T. Kindred, Effie Kalfagianni, and Christine Lee, for their assistance in adding results concerning the crosscap number to the table.

Paolo Lisca discovered many new quasipositive knots.

Lukas Lewark caught several errors in the table and alerted us to several recent results concerning postivity and concordance order that needed to be added to the table.

Duncan McCoy used computer searches to find low genus surfaces in the four-ball bounded by knots. This resolved the four-genus of over 600 11 and 12 crossing knots. See Arxiv preprint for details.

Mark Brittenham has contributed a significant amount of new data regarding the unknotting number and topological four-genus.

Alexandra Kjuchukova assisted us with the data on bridge numbers (including the computation of all bridge numbers for 12-crossing knots, that resulted from her joint work with Blair, Velazquez, and Villanueva.

Jesse Hamer has updated and revised all the braid data, including adding descriptions of (strongly) quasi-positive braids. He has also checked the orientation of the braids. His contributions are based, in part, on his joint work with Tetsuya Ito and Keiko Kawamuro.

Slaven Jabuka and Tynan Kelly provided us with the nonorientable four-genus of all 8 and 9 crossing knots.

Noboru Ito contributed to the addition of the 3D-Clasp number to the database.

Heegaard Floer knot invariants, including tau, epsilon, nu, and "L-space" were computed using a program written by Zoltan Szabó, available at: HFKcalc.

Tunnel numbers for 11 and 12 crossing alternating knots, and many nonalternating knots, were provided by Felipe Castellano-MacĂ­as and Nicholas Owad: arXiv preprint.

Many new results concerning the polygon index (stick number) and super bridge index were provided by Thomas Eddy and Clayton Shonkwhiler. arXiv preprint.

Slaven Jabuka has provided use with details about the non-orientable four-genus, based on his joint work with Tynan Kelly. arXiv preprint.

Taizo Kanenobu has pointed out the relevance of the work of Goda-Hirasawa-Yamamoto and Dasbach-Lowrance in resolving the fact that 11n183 is almost alternating and that 11n95 is not almost alternating.

Dirk Schuetz assisted us in correcting the signs of Rasmussen invariants to be consistent with knot orientations as presented by the PD notation. Se-Goo Kim provided us with further assistance in checking orientation issues.

Stepan Orevkov performed all the initial computations related to the four-genus of links, computing lower bounds based on signatures, the Arf-Robertello invariant and the slice Bennequin inequality. He found upper bounds using a computer search for low genus surfaces.

Stepan Orevkov has now provided us with the braid index and minimal width braid represenations of each link. He has also found quasipositive braid representations for each link (or its mirror image) when such representations exist.

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