FILE- In this Oct. 2, 2008 file photo, New York Mayor Michael Bloomberg speaks to reporters about the rebuilding of the World Trade Center site in New York. Bloomberg, who once shied away from his predecessor’s suggestion that the entire World Trade Center site should be made into a "soaring, monumental" tribute now chairs the foundation responsible for the September 11 memorial. (AP Photo/Seth Wenig, file) The Associated Press FILE- In this Dec. 22, 2010 file photo, New York City Mayor Michael Bloomberg, left, speaks before helping to plant the Survivor Tree at the World Trade Center site in New York. Bloomberg, who once shied away from his predecessor’s suggestion that the entire World Trade Center site should be made into a "soaring, monumental" tribute now chairs the foundation responsible for the September 11 memorial. At right is Christopher Ward, the Executive Director of the Port Authority of New York and New Jersey. (AP Photo/Mark Lennihan, file) The Associated Press FILE- In this Jan. 14, 2004 file photo, New York City Mayor Michael Bloomberg sits in front of an artist rendering of the winning design for the World Trade Center site memorial: Reflecting Absence, during a press conference to unveil the memorial in New York. Bloomberg, who once shied away from his predecessor’s suggestion that the entire World Trade Center site should be made into a "soaring, monumental" tribute now chairs the foundation responsible for the September 11 memorial. (AP Photo/Mary Altaffer, file) The Associated PressNEW YORK (AP) — For many, Rudolph Giuliani is the mayor they will forever associate with the Sept. 11 attacks. But Michael Bloomberg's tenure has been entwined with the rebuilding that followed, and it will form a part of his legacy.Bloomberg argued after the attacks that he was best qualified to help the city recover because of his business background. Once elected, he offended some victims' families with his pragmatic and sometimes cold style.Over the years, he has deepened his policy involvement in the rebuilding of the trade center and the creation of a national memorial. He's now leader of the foundation responsible for it.Hunter College political science professor Kenneth Sherrill says people will remember his tenure as a backdrop to 9/11 recovery.