Who is Petra from Fugitive Pieces and what is their importance?

Petra was the beautiful, blue-eyed, ypung woman with whom Ben fell in love. He met Petra on Idhra Island in Greece, and although, Petra couldn't decide what she wanted to do with her life..... she knew she didn't want to go home. During the three three months she spent traveling, Petra swam daily and talked about her past. Ben studied the lines, scents, and sounds of her body until he could identify her in darkness. Needless to say, they do not end up together, and in the end, Ben sees her with another man.