The Greek alphabet, sure, but Hagia Sophia? The one that was ordered to be built by a Roman emperor and consecrated by a Christian bishop from Antioch? I would describe it as Roman, Byzantine, or Ottoman before I would describe it as Greek.
Even so, we do have clear examples of Greek Culture, since practically the beginning of records, even if that culture has been influenced by other cultures over time (as most cultures are).
Even conquered peoples generally maintain their culture as the culture or sub-culture of whatever society they live in. The governments might fall, but the people's culture usually lives on.
I meant how both of its designers were Greek, and it was built in a majority-Greek city as an Eastern Orthodox church (which wasn't specifically Greek but was different from western Roman). I'm not sure about the emperor or the bishop, but they were born in Tauresium and Arabissos respectively, so I guess Thrace and Armenia Minor then.