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Gluck twist and unknotting of satellite $2$-knots

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arxiv 2009.07353 v2 pith:WSZNG4B4 submitted 2020-09-15 math.GT

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keywords satelliteknotsdescriptiongluckknottwistcertainchange
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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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  1. More Exotic $\mathbb{RP}^2$-knots and Homotopy Spheres

    math.GT 2025-07 conditional novelty 7.0 of 10

    For every integer s, the branched double cover of the roll-spun Montesinos knot K(2,3,|6s+1|) is a homotopy 4-sphere, giving infinitely many exotic topologically unknotted RP^2-knots in S^4 with all odd Seiberg-Witten...

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