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Mar 6, 2014 at 11:52 history edited Tom Goodwillie CC BY-SA 3.0
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Mar 6, 2014 at 4:26 comment added Ryan Budney The PL triangulations literature isn't very easy to search. There's a bunch of Germans that might have quick references for you but as far as I know they don't contribute here. Udo Pachner or Ulrich Pinkall might be good people to ask. Maybe Ed Schwartz at Cornell?
Mar 6, 2014 at 4:19 history edited Tom Goodwillie CC BY-SA 3.0
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Mar 6, 2014 at 4:01 comment added Ryan Budney Okay, the question makes sense to me now. So if we were to take the $M_i$'s to simply be all the top-dimensional simplices, the issue that fails (potentially) is the niceness criterion, specifically (2). You could get possible intersections of higher co-dimension.
Mar 6, 2014 at 3:52 history edited Tom Goodwillie CC BY-SA 3.0
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Mar 6, 2014 at 2:43 comment added Ryan Budney It looks like an impossible demand to me. If the $M_i$'s are contained in simplices of a fixed triangulation they would have to be simplices, but then it would be impossible for them to intersect in co-dimension zero manifolds. Maybe this isn't exactly the question you intended?
Mar 6, 2014 at 2:12 history asked Tom Goodwillie CC BY-SA 3.0