At the end of WWII, why was the fate of Poland so important to the US and the Soviet Union?

The fate of
Poland was very important to both the United States and the Soviet Union, though the Soviet
Union managed to maintain control of Poland. The war against the Nazis had left Stalin's army
quite weak, and he was aware of Western hostility against his regime. Stalin desired a buffer
state between the Soviet Union and the West. Stalin even envisioned this as early as 1939, when
the Soviet Union invaded eastern Poland at the same time the Nazis invaded the western side.
Stalin ordered many captured Polish officers killed in the Katyn Forest, as these people would
form the leadership of any new Polish state. Stalin did not back the Polish government in exile
in London, but rather a puppet state which he appointed after the Red army "liberated"
the country. Stalin's desire for a weak Poland may have also stemmed from a small war fought
between Poland the newly formed Soviet Union from 1919€“1921.

Roosevelt,
while enjoying the support during the war of a very vocal Polish lobby,...