Timeline for Reference for a fact (?) on homeomorphic knot complements

7 events

when toggle format	what		by	license	comment
Nov 18, 2014 at 19:25	history	edited	Ryan Budney	CC BY-SA 3.0	a little more detail on the "promotion" step.
Oct 24, 2014 at 20:59	comment	added	Ryan Budney		Yes, that PL 3-manifolds admit unique smooth structures is an old theorem. I think perhaps Munkres was maybe the first to observe this in 1960 but it might go back further. Munkres result applies in any dimension. He formulated his work in the language of obstruction theory. I think Thurston gives a write-up of his version of this result in his book. You could also approach this from the Kirby-Siebenmann perspective. Hamilton gave a proof that 3-manifolds have unique PL structures and smoothings this way in 1976. See: math.cornell.edu/~hatcher/Papers/TorusTrick.pdf
Oct 24, 2014 at 20:51	vote	accept	Malte
Oct 24, 2014 at 20:51	comment	added	Malte		Thanks, this looks like exactly what I was looking for! I must admit I am still wondering how Moise's theorem implies that every 3-manifold has a unique smooth structure – it seems that every PL 3-manifold needs a unique smooth structure then – but this should be traceable even by me (or so I hope).
Oct 24, 2014 at 20:29	history	edited	Ryan Budney	CC BY-SA 3.0	rewrite it to be more direct.
Oct 24, 2014 at 20:20	history	edited	Ryan Budney	CC BY-SA 3.0	added 308 characters in body
Oct 24, 2014 at 20:09	history	answered	Ryan Budney	CC BY-SA 3.0