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On 2-knots and connected sums with projective planes

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Abstract

In this paper, we generalize a result of Satoh to show that for any odd natural n, the connected sum of the n-twist spun sphere of a knot K and an unknotted projective plane in the 4-sphere is equivalent to the same unknotted projective plane. We additionally provide a fix to a small error in Satoh’s proof of the case that K is a 2-bridge knot.

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Acknowledgements

The author would like to thank his advisors Alex Zupan and Mark Brittenham for all their help, suggestions, and support throughout the process of writing this paper.

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  1. University of Nebraska-Lincoln, Lincoln, USA

    Vincent Longo

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  1. Vincent Longo
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Correspondence to Vincent Longo.

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Longo, V. On 2-knots and connected sums with projective planes. Geom Dedicata 207, 23–27 (2020). https://doi.org/10.1007/s10711-019-00484-8

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