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 degrees.
Simon's conjecture for 2-bridge knots
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abstract
It is conjectured that for each knot $K$ in $S^3$, the fundamental group of its complement surjects onto only finitely many distinct knot groups. Applying character variety theory we obtain an affirmative solution of the conjecture for a class of small knots that includes 2-bridge knots.
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More Exotic $\mathbb{RP}^2$-knots and Homotopy Spheres
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 degrees.