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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 1st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something -- not done yet but I need to save <a href="https://ncatlab.org/nlab/revision/triangulation+theorem/1">v1</a>, <a href="https://ncatlab.org/nlab/show/triangulation+theorem">current</a>

   starting something – not done yet but I need to save

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 1st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexIt seems that Cairn's and Whitehead's proofs work already for $C^1$-differentiable manifolds, not just smooth manifolds. Is that right? <a href="https://ncatlab.org/nlab/revision/diff/triangulation+theorem/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/triangulation+theorem/2">v2</a>, <a href="https://ncatlab.org/nlab/show/triangulation+theorem">current</a>

   It seems that Cairn’s and Whitehead’s proofs work already for $C^1$-differentiable manifolds, not just smooth manifolds. Is that right?

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeAug 1st 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThis comment <https://mathoverflow.net/questions/139339/voronoi-cells-and-the-dual-complexes-in-riemannian-manifolds/177199#177199> seems to give a counterexample to the 1961 proof by Cairns (not Cairn).

   This comment https://mathoverflow.net/questions/139339/voronoi-cells-and-the-dual-complexes-in-riemannian-manifolds/177199#177199 seems to give a counterexample to the 1961 proof by Cairns (not Cairn).

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 1st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the pointer. I have added a warning [here](https://ncatlab.org/nlab/show/triangulation+theorems+--+references#Cairns61).

   Thanks for the pointer. I have added a warning here.