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Would it be worth making a new tag ? While certainly related to classical Morse theory (which already has a tag), most of the technical tools of DMT are quite different, and the literatures are quite distinct. It looks like there are 19 existing questions that mention it.

I would be happy to take care of the re-tagging (incremental, of course, to avoid flooding the front page).

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    $\begingroup$ Some of those 19 questions have only a brief mention of discrete morse theory -- sometimes only in the answers. It looks maybe only 8 or 9 of those threads deserve a discrete-morse-theory tag. But that's substantial enough to create a tag. $\endgroup$
    – Ryan Budney
    Commented Sep 19, 2014 at 15:07

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A tag with 19 questions is already a reasonable size. I thus think (abstractly at least, I know next to nothing about the subject itself) this is a good idea, and generally speaking think that this way to create tags (i.e., identifying a need that exists on the site and fill it) is a good one.

Please keep in mind that tags have tag wikis. It would be great if you could write at least a tag wiki excerpt (the text that is shown when hovering over the tag and in the list of tags) when you create the tag.

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