Spineless 5-manifolds and the deformation conjecture

Michael Freedman; Vyacheslav Krushkal; Tye Lidman

Spineless 5-manifolds and the deformation conjecture

Geometric Topology 2025-12-02 v3

Authors: Michael Freedman , Vyacheslav Krushkal , Tye Lidman

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.

Keywords

smooth 4-manifolds surfaces and embeddings holonomy

Cite

@article{arxiv.2401.03498,
  title  = {Spineless 5-manifolds and the deformation conjecture},
  author = {Michael Freedman and Vyacheslav Krushkal and Tye Lidman},
  journal= {arXiv preprint arXiv:2401.03498},
  year   = {2025}
}

Comments

7 pages. Version 2 is a substantial revision: the main theorem is strengthened, and an open question is formulated about the existence of exotic smooth structures on certain 4-manifolds. Version 3: improved exposition, updated references

Spineless 5-manifolds and the deformation conjecture

Abstract

Keywords

Cite

Comments

Related papers