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On the fibration of augmented link complements

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Abstract

We study the fibration of augmented link complements. Given the diagram of an augmented link we associate a spanning surface and a graph. We then show that this surface is a fiber for the link complement if and only if the associated graph is a tree. We further show that fibration is preserved under Dehn filling on certain components of these links. This last result is then used to prove that within a very large class of links, called locally alternating augmented links, every link is fibered.

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Acknowledgments

I am very grateful to Alan Reid for his guidance during my graduate program. I am also thankful to Cameron Gordon for helpful conversations and João Nogueira and Jessica Purcell for their comments on an early draft of this work. Finally I would like to thank the referee for his careful reading of this paper and his many comments which helped improve it.

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  1. Department of Mathematics, Universidade Federal do Ceará, Av. Humberto Monte s/n, Campus do Pici, Bloco 914, Fortaleza, Ceará, 60455-460, Brazil

    Darlan Girão

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  1. Darlan Girão
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Correspondence to Darlan Girão.

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Girão, D. On the fibration of augmented link complements. Geom Dedicata 168, 207–220 (2014). https://doi.org/10.1007/s10711-012-9826-x

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