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See Andy Putman's first comment on mathoverflow.net/questions/24970/… -- he cites McMillan for the fact that it has the standard PL structure, and then Munkres to show that this implies its smooth structure is standard.
It's probably better to say Conway rediscovered the skein relation -- it's at the end of section 12 ("Miscellaneous theorems") of Alexander's original paper, but apparently nobody noticed this for decades.
