None.

The Mesoamericans and Amerindians came from east Asian populations 10-20,000 years ago (according to all genetic and archeologic evidence). They were smart, capable people that developed their own sophisticated languages, cultures and architectures, just like other people on the planet did. They did not need to be influence by "advanced" cultures from India or Sumeria, since they were just as smart and just as capable as those peoples. 600 years ago, for example, the largest city in America was as big as London was at the same time.

It is just as valid to wonder how the Sumerians and Tamils were influence by Mayan visitors from long ago.
Source(s):
http://en.wikipedia.org/wiki/Models_of_migration_to_the_New_World

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