The police have been the personal trainer-dancer boyfriend of murdered dancer Catherine Woods. Bronx-born Paul Vincent Cortez had once thrown her against a wall during a fight, according to sources. Woods was brutally killed in her Upper East Side apartment on Sunday, and sources also say that skin was found under her fingernails. Cortez and Woods while he trained her at the Upper East Side New York Sports Club; the Post says Cortez recently worked at Equinox. The other suspect in the case has been Woods's ex-boyfriend and roommate David Haughn, who found the body, but so far, his story has held up. The Daily News, though, proposes a murder triangle story, with Haughn allegedly engaged to Woods earlier this year and jealousies between the two men over Woods as a motive.