Spineless 5-manifolds and the deformation conjecture

Michael Freedman; Vyacheslav Krushkal; Tye Lidman

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arXiv · 2401.03498

Spineless 5-manifolds and the deformation conjecture

Michael Freedman·Vyacheslav Krushkal·Tye Lidman

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Abstract

We construct a compact PL 5-manifold $M$ (with boundary) which is homotopy equivalent to the wedge of eleven 2-spheres, $\vee^{}_{1 1}S^2$, which is "spineless", meaning $M$ is not the regular neighborhood of any 2-complex PL embedded in $M$. We formulate a related question about the existence of exotic smooth structures on 4-manifolds which is of interest in relation to the deformation conjecture for 2-complexes, also known as the generalized Andrews-Curtis conjecture.

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Michael Freedman, Vyacheslav Krushkal, Tye Lidman. 2024-01-07. Spineless 5-manifolds and the deformation conjecture. https://arxiv.org/abs/2401.03498

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