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Parity in knot theory and graph-links

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Abstract

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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Authors and Affiliations

  1. Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow, Russia

    D. P. Ilyutko & I. M. Nikonov

  2. Delone Laboratory of Discrete and Computational Geometry, P. G. Demidov Yaroslavl State University, Yaroslavl, Russia

    D. P. Ilyutko & I. M. Nikonov

  3. Faculty of Science, Peoples’ Friendship University of Russia, Moscow, Russia

    V. O. Manturov

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  1. D. P. Ilyutko
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  3. I. M. Nikonov
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 41, Topology, 2011.

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Ilyutko, D.P., Manturov, V.O. & Nikonov, I.M. Parity in knot theory and graph-links. J Math Sci 193, 809–965 (2013). https://doi.org/10.1007/s10958-013-1499-y

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