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Topological Properties of a Class of Higher-dimensional Self-affine Tiles
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 4 / December 2019
- Published online by Cambridge University Press:
- 03 May 2019, pp. 727-740
- Print publication:
- December 2019
-
- Article
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We construct a family of self-affine tiles in
$\mathbb{R}^{d}$ (
$d\geqslant 2$) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in 
$\mathbb{R}^{2}$, and its extension to 
$\mathbb{R}^{3}$ by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.
