We construct a geometrically self-similar Cantor set X of genus 2 in
R3. This construction is the first for which the local genus is
shown to be 2 at every point of X. As an application, we construct, also
for the first time, a uniformly quasiregular mapping f:R3βR3 for which the Julia set J(f) is a genus 2 Cantor set.Comment: 20 pages, 6 figure