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Infinite genus surfaces and irrational polygonal billiards

Ferran Valdez

Number 58
Author Jose Ferran Valdez-Lorenzo
Project B09
Year 2009

We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus topological real surface with exactly one end.

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