Would america have lost ww2 if britain had lost the battle of britain?
There are a lot of crucial battles in that war. But the US would not have lost WW2 in a total sense. Germany would not have been in a position to invade the US for several years after conquering Europe and Russia. In that time the US would have built up a huge Navy and Air Force, either in response to the Japanese invasion, or if that didn’t happen, in response to the aggressive posturing of Germany. So Germany would not have been able to seriously threaten North America, the logistics would have been prohibitive. So instead the cold war would have been Germany versus the US. In fact, it’s much more likely that Germany and Japan would have a falling out before any significant action was taken against mainland USA.