# Tiling billiards and Dynnikov's helicoid

@inproceedings{ParisRomaskevich2021TilingBA, title={Tiling billiards and Dynnikov's helicoid}, author={Olga Paris-Romaskevich}, year={2021} }

Here are two problems. First, understand the dynamics of a tiling billiard in a cyclic quadrilateral periodic tiling. Second, describe the topology of connected components of plane sections of a centrally symmetric subsurface S⊂ T3 of genus 3. In this note we show that these two problems are related via a helicoidal construction proposed recently by Ivan Dynnikov. The second problem is a particular case of a classical question formulated by Sergei Novikov. The exploration of the relationship… Expand

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