Gluck twist and unknotting of satellite $2$-knots

Seungwon Kim

Gluck twist and unknotting of satellite $2$-knots

Geometric Topology 2020-10-27 v2

Authors: Seungwon Kim

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.

Keywords

gluck twist satellite 2-knots 4-manifold diffeomorphism type unknotting real projective plane

Cite

@article{arxiv.2009.07353,
  title  = {Gluck twist and unknotting of satellite $2$-knots},
  author = {Seungwon Kim},
  journal= {arXiv preprint arXiv:2009.07353},
  year   = {2020}
}

Comments

13 pages, 12 figures, Comments welcome!

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