  We generalize a discovery of Kasahara and show that the Jones representations
of braid groups, when evaluated at $q = -1$, are related to the action on
homology of a branched double cover of the underlying punctured disk.
  As an application, we prove for a large family of pseudo-Anosov mapping
classes a conjecture put forward by Andersen, Masbaum, and Ueno by extending
their original argument for the sphere with four marked points to our more
general case.
