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Murasugi decomposition and periodic alternating links

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Let L be a prime non-splittable alternating oriented link in \(S^{3}\). Claude Weber and the second author showed that the collection of Murasugi atoms and the adjacency graph of Murasugi decomposition are topological invariants of L. As a consequence, we note that if L has a q-periodic alternating diagram then the adjacency graph admits an automorphism of order q and each Murasugi atom of L is either q-periodic or occurs a multiple of q times in the atoms collection of L. We apply this fact to study the leading coefficient of the Conway polynomial of this type of links.

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Acknowledgements

We wish to thank the referees for their corrections and very relevant suggestions and to Ana M. Porto for improvements.

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Authors and Affiliations

  1. Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, 28040, Madrid, Spain

    Antonio F. Costa

  2. Section de mathématiques, Université de Genève, CP 64, 1211, Geneva 4, Switzerland

    Cam Van Quach Hongler

Authors
  1. Antonio F. Costa
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  2. Cam Van Quach Hongler
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Corresponding author

Correspondence to Antonio F. Costa.

Additional information

To Professor María Teresa Lozano on the occasion of her 70th birthday.

A. F. Costa partially supported by the project MTM2014-55812-P.

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Costa, A.F., Van Quach Hongler, C. Murasugi decomposition and periodic alternating links. RACSAM 112, 793–802 (2018). https://doi.org/10.1007/s13398-017-0479-3

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