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<p>We study tiling spaces in the diffeological context. We prove some basic diffeological properties for tiling spaces and analyze two different fiber bundle structures of tiling spaces over irrational tori. We use the diffeological classification of irrational tori which captures their arithmetical essence to inherit the diffeological equivalence in the context of one-dimensional tiling spaces.</p>

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Tiling spaces are covering spaces over irrational tori

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月24日

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  • Darío Alatorre,
  • Diego Rodríguez-Guzmán

摘要

We study tiling spaces in the diffeological context. We prove some basic diffeological properties for tiling spaces and analyze two different fiber bundle structures of tiling spaces over irrational tori. We use the diffeological classification of irrational tori which captures their arithmetical essence to inherit the diffeological equivalence in the context of one-dimensional tiling spaces.