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On embedding infinite cyclic covers in compact 3-manifolds

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Abstract

We show that there are knots whose infinite cyclic covers do not embed in any compact 3-manifold, answering a question of Jiang et al. (2006).

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References

  1. Jiang B, Ni Y, Wang S, et al. Embedding infinite cyclic covers of knot spaces into 3-space. Topology, 2006, 45: 691–705

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  2. Yang Z. On embedding the infinite cyclic coverings of knot complements into three sphere. Proc Amer Math Soc, 2010, 138: 1153–1157

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, Austin, TX, 78712, USA

    Cameron McA. Gordon

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  1. Cameron McA. Gordon
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Correspondence to Cameron McA. Gordon.

Additional information

Dedicated to Professor Boju Jiang on the Occasion of His 80th Birthday

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Gordon, C.M. On embedding infinite cyclic covers in compact 3-manifolds. Sci. China Math. 60, 1575–1578 (2017). https://doi.org/10.1007/s11425-016-9035-5

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  • DOI: https://doi.org/10.1007/s11425-016-9035-5

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