Gluck twist and unknotting of satellite $2$-knots

Seungwon Kim

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arXiv · 2009.07353

Gluck twist and unknotting of satellite $2$-knots

Seungwon Kim

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Abstract

In this paper, we show that the Gluck twist of certain satellite $2$-knots in a $4$-manifold do not change the diffeomorphism type in three different ways: one is directly from the definition of the satellite $2$-knot, and the other two are by finding an equivalent description of the satellite $2$-knot. Furthermore, using the new description, we gave infinite number of new examples of $2$-knots which are unknotted by connected summing a single standard real projective plane.

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Seungwon Kim. 2020-09-15. Gluck twist and unknotting of satellite $2$-knots. https://arxiv.org/abs/2009.07353

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