multiply connected region

For multiply connected regions with smooth boundary have given a method for mapping the region onto a disc with circular holes.

The algorithm allows the spawning of smaller snakes that lets the model represent multiply connected regions, allowing the formation of holes and islands.

On Canonical Conformal Maps of Multiply Connected Regions, J. L. Walsh and H. J. Landau, Trans.

A separate "molecular" Aharonov-Bohm effect was proposed for nuclear motion in multiply connected regions, but this has been argued to be a different kind of geometric phase as it is "neither nonlocal nor topological", depending only on local quantities along the nuclear path.