Talk:Piecewise-smooth manifold

Context

Added header. —Nils von Barth (nbarth) (talk) 22:44, 5 May 2009 (UTC)[reply]

This article needs more context. A short introduction what the topic is about can help. I came here in search for a software called pdiff. Does this explain some math used in pdiff, or is this unrelated?

77.24.237.81 (talk) 22:38, 7 June 2008 (UTC)[reply]

Sorry for the lack of context – I’ve substantially expanded this, which should provide better context.

AFAICT there is no relation whatsoever between the category PDIFF and any computer program by that name; this is a very technical point in math, and of likely very little interest outside it.

As for other uses of the term, I’ve create a disambiguation page at pdiff; hope this helps!

—Nils von Barth (nbarth) (talk) 22:44, 5 May 2009 (UTC)[reply]

Blank and restart

This article is completely wrong. PDiff does not form a category and thus almost every else stated is false. Just read the first page of the first reference by Jacob Lurie! Or [this MO answer by Tom Goodwillie](https://mathoverflow.net/a/27673). The only reputable source that says otherwise is McMullen, but he, in turn, cites Thurston, who is the very clearest against him. I can't link Thurston, but I quote exercise 3.10.1(a):

"Show that such maps [pdiff] don’t form a group. Thus, piecewise smooth maps serve as bridges between piecewise linear and smooth structures; they don’t work well alone."

A stub consisting of just the bibliography (ex McMullen) would be an improvement on this article. 108.52.140.137 (talk) 16:12, 29 June 2019 (UTC)[reply]

I agree with this comment. I contacted Curtis T. McMullen and he agrees with the fact that there is no meaningful category PDiff. You can have a PDiff manifold by requiring the transition functions to be PDiff, but PDiff is not closed under composition. The Surgeon of Death (talk) 12:24, 19 June 2026 (UTC)[reply]

I cut it down somewhat but am not convinced that its cut-down state is satisfactory. If there is no category PDIFF, what does the title of the article refer to? Merely the class of piecewise-smooth manifolds? If so, the title should be something more like piecewise-smooth manifold, currently a redirect to here. —David Eppstein (talk) 21:47, 21 June 2026 (UTC)[reply]

@David Eppstein: Sorry for the hassle!

I've moved this to Piecewise-smooth manifold, as suggested, corrected the referencing pages, notably [1] and [2], and updated links.

This is a minor enough topic that this page should probably be moved into a section of Piecewise linear manifold, but it's confusing enough that it warrants some mention.

—Nils von Barth (nbarth) (talk) 12:30, 24 June 2026 (UTC)[reply]