The Acropolis of Pergamon is a hill that is still in Pergamon. The Pergamon Altar is a large structure that was moved to Berlin in the late 1800's. Since Erdogna is a Muslim, it does not make sense that he would care about retrieving an altar that contains pictures of Greek gods.
“The White House is denying that Obama accepted an offer from Erdogan to join him at the mosque opening.”
The Foreign Minister of Turkey, Mevlut Cavusoglu, says otherwise.
http://www.aa.com.tr/en/turkey/496476—erdogan-obama-to-open-turkish-mosque-in-us-turkish-fm
I’m an art historian and find you comments concerning the Acropolis of Pergamon to be weak.
The Germans took the Altar off to Berlin and it wasn’t until 1930 that it was opened to the public. The museum building that houses it on an island in the river in Berlin is now closed for repairs and will not reopen until 2020.
The Nazis valued the Altar of Pergamon and had dinners in front of it at the foot of the stairs. To protect it from bomb destruction during the war, they disassembled it and placed it in storage (bomb shelter), which the Russians later found and transferred to Moscow. It was returned to Berlin in 1959.
The sculptural frieze of the altar depicts the war between good and evil, and is believed to be a Gigantomachy. It does not depict any historical event.
As for Erdogan being a Muslim and therefore not caring about retrieving an altar depicting Greek gods, he cares enough to turn Hagia Sophia from a museum into a mosque. Oh, he’ll no doubt cover over the Christian mosaics but whether they are there under plaster won’t concern him: it is the action of repudiating other religions that is important to Erdogan.