All right, krellin, I'll bite.
"Bo, nothing about the defeat of the Indians has caused either the genocide of Indians (i.e. they are STILL here, dumbass) or the extinction of their culture."
The "Indians" - which apparently still doesn't mean people from India - were not "defeated," they were, as I like to say, accidentally exterminated. Between the time that Columbus arrived in the Caribbean and dubbed the people he saw as "Indians" and when the pilgrims began writing history, this little bug that your pint-sized brain might not be able to comprehend called smallpox came about. And what did it do? Well, besides eradicating 96% of the "Indians" in Massachusetts - which was so densely populated that Giovanni da Verrazzano said that, along with the rest of the eastern coastline, he could smell bonfires from a hundred miles offshore. Otherwise, the disease took out over 90% of the "Indians" nationwide, which is nothing. So it was no big deal.
For reference, the Black Plague - emphasis on the word "plague" - killed between 30% and 50% of Europeans over the course of 200-300 years. In the five years after 1342, when it is believed to have found its way to Europe on a trade ship, it killed nearly 20% of the European population. That's a lot. It devastated Europe. The classical age never arose again and, for all intents and purposes, that culture died and is only studied but rarely practiced today in favor of the Enlightenment.
The smallpox plague that went across North America is, consequently, the worst mass epidemic of a disease in known human history. The Europeans walked into a land where the people were already dying in a sort of apocalyptic event - think Walking Dead except that they didn't really have the strength to fight back the majority of the time. That's not defeat, that's just horrifying.
"I see no movement within the US to extinguish Indian culture."
WEELLLLLLLLLLLL you should look harder. Smallpox alone isn't genocide, you fucking idiot. See, the highest estimates suggest that North America was home to about 100 million people before Europeans showed up. The lowest say that it was home to about 12 million. Either way, the population by 1900 in all of North America (including Canada and Mexico, and, at the time, the largely untouched swathes of Alaska) was no more than 200,000-250,000. How it got there is by a) burning and pillaging villages, b) praying towns, where they literally grabbed the next generation of "Indians" and dropped them in Puritan-style homes with Bibles and an oil lantern and just left them, c) reservations, which picked up "Indians" from their homes and dropped them somewhere where it was convenient for you and I to not notice them anymore, or d) the fucking Trail of Tears and countless other historical events like it that evidently you haven't heard of. By the way, 250,000 isn't a lot of people. That's about as many people that live in Grand Rapids. Spread them continent-wide. Take that and split it up into hundreds, if not thousands, of surviving tribal groups and you have a pretty stupidly fucking genocidal scenario where countless tribes could be classified as at immediate risk of extinction according to the Endangered Species Act - you know, since you seem to feel like "Indians" are little more than animals anyway.
How many are there today? 5.2 million. Obviously, that's a lot higher. I can't wait to hear you argue that that somehow implies that they're not subject genocide today. First off, they still live predominantly in these reservations, and 11 of the 20 poorest counties in the whole of the US are reservation counties. Here's a fun example from a source I can see you masturbating to, hopefully in private:
http://www.businessinsider.com/bi-dangerous-indian-reservation-2012-2
Here's another, but I don't think even you can jerk off twice in a row:
http://www.forbes.com/sites/realspin/2014/03/13/5-ways-the-government-keeps-native-americans-in-poverty/#621ee0176cc6
I'm bored of teaching you the most basic history that fucking PBS Kids writes about and you're stroking yourself, so I'm done.