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Cantor tree surface

Fractal with infinite genus

The bark of a fractal tree, splitting in two directions at each branch point, forms a Cantor tree surface. Drilling a hole through the tree at each branch point would produce a blooming Cantor tree.

In dynamical systems, the Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of handles.

References

(1995). "Topologie des feuilles génériques". [[Annals of Mathematics]].
(2004). "Dynamics of foliations, groups and pseudogroups". Birkhäuser Verlag.

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