The salient crossings of a crown diagram

J Williams

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arXiv · 2202.05418

The salient crossings of a crown diagram

J Williams

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Abstract

A crown diagram of a smooth, closed oriented 4-manifold can be thought of as the projection of a link in the product of a closed surface and the circle, with chords in the circle direction connecting the strands of each crossing. This paper uses a straightforward assignment of integers to these chords to show that the smooth structures on the topological 4-manifold underlying a pair of Fintushel-Stern knot surgery 4-manifolds which are known to have the same Seiberg-Witten invariant are not isotopic. A natural question is to determine if the argument may be strengthened to show these manifolds are not diffeomorphic.

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J Williams. 2022-02-11. The salient crossings of a crown diagram. https://arxiv.org/abs/2202.05418

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