Corpus ID: 231986567

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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References

SHOWING 1-10 OF 26 REFERENCES
Trees and flowers on a billiard table
  • 2
Periodicity and ergodicity in the trihexagonal tiling
  • 5
  • PDF
Dimers and amoebae
  • 391
  • PDF
...
1
2
3
...