Booker winner A.S. Byatt (”Possession”) ends the quartet on English life she began in 1979’s ”The Virgin in the Garden” with A Whistling Woman, a bold, brainy eulogy to the late ’60s. Heroine Frederica Potter — now a single mother in her 30s — lands a job hosting ”Through the Looking-Glass,” a groovily postmodern talk show. Frederica’s fractured home, work, and love life reflect Byatt’s primary concern, the splintering of self and society. But the story proves fragmented too, as myriad subplots — including one about hippies who create an ”anti-university” and another about a cult headed by a dangerous schizophrenic — barely come together for the fiery finale. The plethora of characters sometimes drowns out the ”whistling woman” (presumably free-spirited Frederica), but Byatt’s clashes between the intimate and the intellectual make for a raucous, lively work.