##
**The classification of alternating links.**
*(English)*
Zbl 0809.57002

The paper contains the detailed proof of the famous “flype conjecture” proposed by P. G. Tait in 1898. It says that two reduced, prime, oriented and alternating diagrams of isotopic links can be transformed into each other by flypes. A corollary states that \(\pm\) amphicheirality can also be effected by flypes between one such diagram and its mirror image in the projection plane, given appropriate orientations. The long and intricate proof is mainly geometric and combinatorial. It would be futile to attempt to give a description here. There is, however, one vital point in the structure of the proof where an argument is needed which makes use of the new polynomial invariants. The work rests on several previous results obtained mainly by the two authors.

Reviewer: G.Burde (Frankfurt / Main)

### MSC:

57M25 | Knots and links in the \(3\)-sphere (MSC2010) |