Simple spines of homotopy 2-spheres are unique

Patrick Orson; Mark Powell

doi:10.1112/plms.12583

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arXiv · 2208.04207

Simple spines of homotopy 2-spheres are unique

Patrick Orson·Mark Powell

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Abstract

A locally flatly embedded $2$-sphere in a compact $4$-manifold $X$ is called a spine if the inclusion map is a homotopy equivalence. A spine is called simple if the complement of the $2$-sphere has abelian fundamental group. We prove that if two simple spines represent the same generator of $H_2(X)$ then they are ambiently isotopic. In particular, the theorem applies to simple shake-slicing $2$-spheres in knot traces.

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Patrick Orson, Mark Powell. 2022-08-08. Simple spines of homotopy 2-spheres are unique. https://doi.org/10.1112/plms.12583

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