Splitting number of augmented links

Author:

Girao Darlan1ORCID

Affiliation:

1. Department of Mathematics, Universidade Federal do Ceará, Av. Humberto Monte, s/n, Campus do Pici, Bloco 914, Fortaleza 60455-760, Brazil

Abstract

We completely determine the splitting number of augmented links arising from knot and link diagrams in which each twist region has an even number of crossings. In the case of augmented links obtained from knot diagrams, we show that the splitting number is given by the size of a maximal collection of Boromean sublinks, any two of which have one component in common. The general case is stablished by considering the linking numbers between components of the augmented links. We also discuss the case when the augmented link arises from a link diagram in which twist regions may have an odd number of crossings.

Funder

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico

Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

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