  It is well known that baby Mandelbrot sets are homeomorphic to the original
one. We study baby Tricorns appearing in the Tricorn, which is the
connectedness locus of quadratic anti-holomorphic polynomials, and show that
the dynamically natural straightening map from a baby Tricorn to the original
Tricorn is discontinuous at infinitely many explicit parameters. This is the
first known example of discontinuity of straightening maps on a real
two-dimensional slice of an analytic family of holomorphic polynomials. The
proof of discontinuity is carried out by showing that all non-real umbilical
cords of the Tricorn wiggle, which settles a conjecture made by various people
including Hubbard, Milnor, and Schleicher.
