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Graph-Links: The State of the Artстатья
- Авторы: Ilyutko D.P., Manturov V.O., Nikonov I.M.
- Сборник: New Ideas in Low Dimensional Topology
- Серия: Series of Knots and Everything
- Том: 56
- Год издания: 2015
- Место издания: World Scientific Publishing Co (Singapore)
- Первая страница: 189
- Последняя страница: 236
- DOI: 10.1142/9789814630627_0006
- Аннотация: In this paper we discuss the latest achievements in graph-link theory created by the first two authors in 2008–2009. This theory is a far-reaching generalization of classical and virtual knot theory and originates from the notion of the intersection graph (of a chord diagram). For a given graph a chord diagram having this graph as its intersection graph may not exist, however many invariants of classical and virtual knots can be extended to the theory of graph-links, in particular, Khovanov homology. Here we construct invariants of graph-links, many of them are based on the notion of parity due to the second author.We derive new properties of graph-links which do not exist in the realizable case, and present non-realizable graph-links (i.e. such graph-links which have no representative realizable by a chord diagram), define an orientation for graph-links and construct the theory of Khovanov homology for graph-links.
- Добавил в систему: Ильютко Денис Петрович