## Return to Answer

2 fixing typos, and hyperlinking the title.

I posted a paper on the arXiv: , Group Width which answers this question for manifolds of dim >3 $>3$ with sufficiently complicated fundamental group (there will be no finite set of blocks). As Greg Kupeberg Kuperberg said, there are many interesting variations which remain open and are a nice chalange challenge to technique, e.g. the case of simply connected manifolds.

1

I posted a paper on the arXiv: Group Width which answers this question for manifolds of dim >3 with sufficiently complicated fundamental group (there will be no finite set of blocks). As Greg Kupeberg said, there are many interesting variations which remain open and are a nice chalange to technique, e.g. the case of simply connected manifolds.
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