# To Do

From Knot Atlas

- Update this To Do list.
- Make sure all KnotAtlas associated software is in either the KnotTheory or KnotAtlas svn repositories, and document how to get programs from svn. See Category:Software.
- Remove all the splicing programs.
- Fix the whitespace in formulas containing symbols from dbnsymb; see e.g. The_Jones_Polynomial#eq:KBDef.

## Contents |

## Knot Atlas issues

- Link to us from relevant pages on wikipedia and elsewhere.
- Add "comment" hooks near each of the sections on the knot pages.

### Pages to write

- Further edit How you can contribute.
- Finish Extending/Modifying KnotTheory`.
- Prepare List of Modules in KnotTheory`.
- Document "The A2 invariant", "The G2 invariant" and "other quantum invariants".

### More complicated projects

- Identify torus knots.
- should we have an 'identify this knot' function in KnotTheory`? How to implement it?
- one way to do this would be to: 1) triangulate the knot/link complement then 2) use the Rubinstein algorithm to find the connect-sum decomposition 3) use the Jaco-Rubinstein algorithm to compute the JSJ-decomposition of the prime parts and identify the Seifert-fibred bits and 4) use SnapPea to identify the hyperbolic parts. (1) is implemented in several places such as Orb and Knotscape, (2) is implemented in the software called Regina, by Ben Burton (do a Google search for "Regina sourceforge" (3) is not yet implemented and (4) has been implemented for a long time now, in SnapPea's isometry checker. Perhaps you would like to use a less big hammer for this problem, though? -ryan

- Clarify orientation issues, especially for links.
- As in, if you reverse the orientation of a particular strand, do you get the same oriented link? The above JSJ schema gives a systematic way to do this.

- Extend tables beyond 11 crossings.
- Add pages on rational knots and other classes of "special" knots.
- Add a page for "sporadic" special knots.

### Data to include

- Add Tristram-Levine signatures.
- Chiral? Invertible?
- More generally, list the full symmetry group of the knot (isotopy classes of diffeomorphisms of the pair (S^3,K) and describe whether or not it can be realized as a subgroup of Diff(S^3,K), the fixed point sets, how it acts on the orientations of S^3 and K respectively, etc... If you're going to start including symmetry data, why not do it all? Again the JSJ-schema I outlined above is one way to approach this. -ryan

- Indicate which knots are the components of given links.
- Add something about hyperbolic invariants.
- "Similar Links" using The Multivariable Alexander Polynomial; add the The Multivariable Alexander Polynomial to the simulated Mathematica sessions.

## Things to calculate

- Compute
*HOMFLYPT*for torus knots -- this has been added to the Upload_Queues. - compute Reshetikhin-Turaev invariants for everything in sight.

## KnotTheory`

- Put the MIT license notice in all the source files. (You can consider this note as MIT licensing for now. If you're one of the contributors, and you didn't complain when we proposed MIT licensing for everything, you can still complain now!)
- Write some functions to generate knot families, taking advantage of ConwayNotation. Pretzel knots, etc.
- Unite
`DrawPD`

and`BraidPlot`

under Draw. - Remove
`Simplify`

from ColouredJones. - Custom knot drawings! Output in ps, TeX, etc.
- Browsable source code for
`KnotTheory``

. - Fix the
`In`/`Out`numbering in Graphical Input. - The makefile incorrectly includes the .svn subdirectories in KnotTheory.zip. (But not in KnotTheory.tar.gz, because there we can use the
`--exclude .svn`

option for tar. What's the corresponding option for zip?)

## katlas software

- Find out if it's possible to eliminate the need for &action=purge when transcluded pages change?
- Tell people about the modifications to ImagePage.php
- made redundant by upgrading medawiki!

- Fix/improve the "disappearing transclusion" tag <ifpageexists>.
- again, made redundant -- use {{:ifexists|||}}

- Replace the "bracket" splicing model by a "templated" one.

## texvc

- can texvc use dvi2bitmap instead of convert? might be much faster? [1]
- alternatively see [2]
- what about a cron job to randomly delete entries from mw_math, and the corresponding png's?

- Apply patches to texvc, for making transparent, font-sizes png in math mode. [3]

## Other things

- Add the Universal Vassiliev Invariant.
- Something about knot colouring.
- Add Ozsvath-Szabo stuff.
- Make all sources public.
- Add Dowker codes for links.

## Papers to consider extracting data from

- Extract data from Stanford's paper [4].
- Extract data from Livingston's paper [5].
- Extract data from Rasmussen's paper, arXiv:math.GT/0402131. (I think this has been done - I imported s-invariant data from KnotInfo. --Scott 02:06, 26 May 2006 (EDT))
- Extract data from Hikami's paper, arXiv:math.GT/0403224.
- Extract data from Stoimenow's paper, arXiv:math.GT/0405076.
- Extract data from De Wit and Links, arXiv:math.GT/0501224, and from De Wit, Ishii and Links, arXiv:math.GT/0405403.
- Extract data from Cha-Livingston's paper, arXiv:math.GT/0503125.
- Extract data from Hirasawa-Teragaito's paper, arXiv:math.GT/0504446.
- Extract data from Cimasoni-Florens' paper, arXiv:math.GT/0505185.
- Extract data from Ashton-Cantarella-Piatek-Rawdon's paper, arXiv:math.DG/0508248.
- Boundary slope data. There's Dunfield's paper, and associated program, arXiv:math.GT/9901120, and also a paper by Hoste and Shanahan arXiv:math.GT/0505442, which contains data for many two component links.
- Extract data from Baldwin-Gillam's paper, arXiv:math.GT/0610167.

Pages with the 'todo-later' template Pages with the 'todo' template