Parity in knot theory and graph-links

D. P. Ilyutko ; V. O. Manturov ; I. M. Nikonov

Contemporary Mathematics. Fundamental Directions, Topology, Tome 41 (2011), pp. 3-163.

Résumé

The present monograph is devoted to low-dimensional topology in the context of two thriving theories: parity theory and theory of graph-links, the latter being an important generalization of virtual knot theory constructed by means of intersection graphs. Parity theory discovered by the second-named author leads to a new perspective in virtual knot theory, the theory of cobordisms in two-dimensional surfaces, and other new domains of topology. Theory of graph-links highlights a new combinatorial approach to knot theory.

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