ScalingStacks

0NG9

Lemma 4.4. For every lasagna filling FF of 𝒮0N​(W1,L,𝕜)\mathcal{S}_{0}^{N}(W_{1};L,\mathbbm{k}), there exists a framed LT⊂∂B4L_{T}\subset\partial B^{4}, such that FF is contained in the image of glueLT\mathrm{glue}_{L_{T}}.

0NGA

Proof. By a small isotopy, we may assume that FF satisfies the assumption of the cutting procedure described above. The statement now follows since cutting, albeit ill-defined, is manifestly a right-inverse to gluing. ∎

Original mathematics by the credited authors. Source collection and HTML conversion remain in progress.

Ciprian Manolescu, Kevin Walker, Paul Wedrich

Original source: arXiv:2206.04616v2