Genus 2 Cantor sets

Publication date: 25 September 2020

Abstract: We construct a geometrically self-similar Cantor set

X

of genus

2

in

m a t h b b R^{3}

. 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 : m a t h b b R^{3} o m a t h b b R^{3}

for which the Julia set

J (f)

is a genus

2

Cantor set.

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