What will be?

[N-Man]

The Cathedral of Saint Sophia is no longer a mosque. The Muslim symbols were removed by Mustafa Kemal Ataturk during the earlier 20th century, and it now serves as a museum. It was indeed captured by the Turks, which are not to be confused with the Arabs, or Saracens. Saracen is the medieval word for Arab.

Build roads. Right. Well, I'm sure one can find an instance of knights participating in public works (not that there was a wealth of those back then) since there wasn't anything like a law that ruled knights to be exempt from working, but this wasn't their main purpose. Knights were not a labour pool to be accessed during public works; those were directed by masons or engineers, and executed by skilled workers in the case of buildings or monuments, and unskilled serfs in the case of simpler things like roads.

You also have to keep in mind that kings in that time had very little control over their knights, especially landless knights as these did not particularly serve any overlord (knights are tied to dukes and kings through their land, not through blood). Also, most of the early crusaders came from places which did not even have kings, such as the Low Countries (modern Belgium and Netherlands, the area between Germany and France which was often quite anarchic and split between various dukes and counts), southern France which was out of the grip of the king of France and ruled by the dukes of Toulouse, as well as Sicily and southern Italy which was ruled by the still-savage Norman dukes. Knights could also set off on crusade precisely because they did not like their overlords; all I'm saying is, kings and lords of all kinds had little influence on what their landless subjects did. They had nothing that tied them to the land, thus nothing that tied them to a kingdom.

This is obviously different from the later crusades, like the third which had Philippe Augustus and Richard Lionheart leading their countries' armies into the middle east, and Saint Louis' crusade (ninth?) to Egypt which was also the same. But by then, the conflict was on: we are no longer talking about what sparked it. The Europeans evidently found other reasons to stay in Palestine once they were in there: like I said, spices, silks and other things which had faded out of European trade since the fall of Rome.