ABSTRACT
In this chapter, the author talks about an alternative way for encoding knots and links (different from planar diagrams and closures of braids). Namely, all knots can be encoded by so-called "atoms" and d-diagrams. Atoms are combinatorial objects that arose several years ago in [Fom] for purposes of classification of integrable Hamiltonian systems of low complexity. d-diagrams are special chord diagrams closely connected with atoms. Atoms play a crucial role for the construction of Khovanov homology. By using this approach, the author proves several theorems on knots and curves: Kauffman-Murasugi's theorem on alternating links, the criterion for embeddability of special graphs, etc. The author also describes a way of encoding knots by words in a finite alphabet via d-diagrams.
