  By means of a nested sequence of some critical pieces constructed by
Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved
by Kahn and Lyubich, we prove that the Julia set of a polynomial is a Cantor
set if and only if each component of the filled-in Julia set containing
critical points is aperiodic. This result was a conjecture raised by Branner
and Hubbard in 1992.
