This repository holds some formalizations of knot theory proofs in lean.
Currently planning on:
- [x] underlying representation of bricks/walls basic
- [x] notion of planar isotopy equivalence basic
- [x] notion of reidemeister move equivalence basic
- [ ] proof that brick/wall notions of equivalency are sufficient (not sure how to do this?)
- [x] definition of tangle tangle
- [ ] tangle surgery or inductive notion of tangle equivalency
- [x] proof of tangle invariance across notions of equivalence tangle
- [x] definition of link link
- [x] definition of knot link
- [x] definition of braid braid
- [ ] definition of permutation, proof that braid is a permutation
Not quite sure about the following:
- [ ] notion of tri-colourability
- [ ] notion of alternating
- [ ] HOMFLY/Jones polynomials
- Prathamesh, T. V. H. (2015). Formalising Knot Theory in Isabelle/HOL. Lecture Notes in Computer Science, 438–452. doi:10.1007/978-3-319-22102-1_29 / prathamesh-t/Tangle-Isabelle