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Spines for spineless 4-manifolds

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Spines for spineless 4-manifolds
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17
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A recent paper of Levine-Lidman gives examples of simply connected 4-manifolds X, homotopy equivalent to a 2-sphere, that do not admit PL spines. In other words, there is no PL (not necessarily locally flat) embedded sphere in X that is a strong deformation retract of X. I will show that a family of the Levine-Lidman examples admit a topological spine—a locally PL sphere that is a strong deformation retract of X. This is joint work with Hee Jung Kim.