During an anti-Muslim diatribe, the former mayor called for Mr. Mamdani to skip the ceremonies. The mayor has said he is going.

They have no memory of the buildings missing from the skyline or airports without security lines. But they have strong feelings about how to regard the legacy of the attacks.

In police shootings in Times Square and at the Brooklyn Bridge, officers had to make split-second decisions in confronting emotionally disturbed people who were violent or threatening violence.