Simply slicing knots

Anthony Conway; Patrick Orson; Mark Pencovitch

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arXiv · 2507.00431

Simply slicing knots

Anthony Conway·Patrick Orson·Mark Pencovitch

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Abstract

Given a simply-connected 4-manifold with boundary the 3-sphere, this paper establishes sufficient conditions for a knot in the boundary to be sliced by a locally flat disc in the 4-manifold, whose complement has finite cyclic fundamental group. In addition, necessary and sufficient conditions are described to ensure that such discs exist stably, that is after taking the connected sum of the 4-manifold with copies of $S^2 \times S^2$.

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Anthony Conway, Patrick Orson, Mark Pencovitch. 2025-07-01. Simply slicing knots. https://arxiv.org/abs/2507.00431

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