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Heegaard genus and rank of augmented link complements

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Abstract

We prove that the rank of the fundamental group of an augmented link complement equals its Heegaard genus. This is achieved by showing that the Heegaard genus equals the number of link components. A straightforward consequence is that these manifolds satisfy a conjecture of Shalen.

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Acknowledgments

The author thanks Jessica Purcell for discussing the subject, CNPq–Brazil (Project 446307/2014-9) and FUNCAP-Brazil (Project PJP-0072-00013.01.00/12) for the financial support.

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  1. Department of Mathematics, Universidade Federal do Ceará, Fortaleza, Brazil

    Darlan Girão

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  1. Darlan Girão
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Correspondence to Darlan Girão.

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Girão, D. Heegaard genus and rank of augmented link complements. Math. Z. 281, 775–782 (2015). https://doi.org/10.1007/s00209-015-1507-7

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  • DOI: https://doi.org/10.1007/s00209-015-1507-7

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