Counterexamples to Allen's conjectures
Abstract
We show that the torus knots T(2,5) and T(2,9) bound smooth M\"obius bands in the 4-ball whose double branched covers are negative definite, giving counterexamples to Conjectures 1.6 and 1.8 of Allen in [New York J. Math. 29 (2023) 1038-1059].
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