**
Below is the ascii version of the abstract for 03-529.
The html version should be ready soon.**Jung, W.
Homeomorphisms of the Mandelbrot Set
(511K, pdf)
ABSTRACT. On subsets E of the Mandelbrot set M , homeomorphisms are
constructed by quasi-conformal surgery. When the dynamics of quadratic
polynomials is changed piecewise by a combinatorial construction, a general
theorem yields the corresponding homeomorphism h: E to E in the parameter
plane. Each h has two fixed points in E , and a countable family of
mutually homeomorphic fundamental domains. Possible generalizations to
other families of polynomials or rational mappings are discussed. The
homeomorphisms on subsets E of M constructed by surgery are extended
to homeomorphisms of M , and employed to study groups of non-trivial
homeomorphisms h: M to M . It is shown that these groups have the
cardinality of the continuum, and they are not compact.