Lernaean knots and band surgery

Belousov, Yu.; Karev, M.; Malyutin, A.; Miller, A.; Fominykh, E.

doi:10.1090/spmj/1687

Lernaean knots and band surgery
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by Yu. S. Belousov, M. V. Karev, A. V. Malyutin, A. Yu. Miller and E. A. Fominykh
Translated by: the authors

St. Petersburg Math. J. 33 (2022), 23-46

DOI: https://doi.org/10.1090/spmj/1687

Published electronically: December 28, 2021

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Abstract:

The paper is devoted to a line of the knot theory related to the conjecture on the additivity of the crossing number for knots under connected sum. A series of weak versions of this conjecture are proved. Many of these versions are formulated in terms of the band surgery graph also called the $H(2)$-Gordian graph.

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