A biographer's life is not an easy one, especially when his subject has preempted the story by producing an autobiography. Playwrights and moviemakers have a special edge in turning the mirror to a flattering angle, but Bob Fosse is the first choreographer to beat his biographer to the punch. Fosse's All That Jazz was a movie musical with a razzle-dazzle half-hour finale showing the showman in the throes of a death brought on by cigarettes, amphetamines, and a hyperkinetic philosophy of ''Gotta Dance! Gotta Dance!''
From his first choreographic show-stopper, ''Steam Heat'' in The Pajama Game (1954), and on through a string of hits that included Damn Yankees, Cabaret, Pippin, and the Academy Award-nominated Lenny, till his death in 1987 while touring a revival of Sweet Charity, Bob Fosse embodied the Go-Go Years. First as a choreographer and the Svengali of his girlfriend and future wife, Gwen Verdon, then as a director on Broadway and in Hollywood, Fosse set the same relentless pace for the artists who served his vision as he did for himself. And the vision being served was focused on one thing sex.
Sex was also, apart from show biz success, the single focus of Fosse's waking life. He got married or took a new mistress according to the requirements of his career or the latest show he had to cast. Readers who look for celebrity biographers to dish out quantities of dirt will find All His Jazz: The Life and Death of Bob Fosse to be a smorgasbord. Yet for all that the man comes across less as a latter-day Don Juan than a kind of male Camille, always on the make but able to fall sincerely in love at the drop of a handkerchief.
Over many pages, however, the effect of Fosse's career-driven sexual fecklessness is not as powerful as it was in the frenetic 123 minutes of All That Jazz. An entire lifetime of giddy exhilaration begins to look like one of Dante's more insidious punishments.
In that regard, Martin Gottfried, the biographer, has the last word. As a prose stylist he may not generate the literary equivalent of ''Steam Heat,'' but his disenchanted coolness provides just the right corrective to the lurid tale he has to tell. B+