For anybody who cares, this site discusses “cult archaeology” http://www.uiowa.edu/~anthro/fantasti/culttopics.html and addresses the topic of transoceanic contact.
See those stars over there? That is the Little Dipper. I’d show you the Big Dipper, but my zipper is stuck.
I think the Egyptians also found out about kites from the Chinese, and used them to build the pyramids. 
The theory about the early Jomon pottery and the Inca is pretty convincing. I mean, what are the odds that two civilizations could independently come up with coil pottery with stripy decoration? The same goes for moundbuilding. Like, how many civilizations do that? So few that there must be a connection.