Topological Properties of a Class of Higher-dimensional Self-affine Tiles

Guotai Deng; Chuntai Liu; Sze Man Ngai

doi:10.4153/S0008439519000237

Topological Properties of a Class of Higher-dimensional Self-affine Tiles

Guotai Deng, Chuntai Liu, Sze Man Ngai

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We construct a family of self-affine tiles in ℝ^d (d ≥ 2) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in ℝ², and its extension to ℝ³ by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.

Original language	English
Pages (from-to)	727-740
Number of pages	14
Journal	Canadian Mathematical Bulletin
Volume	62
Issue number	4
DOIs	https://doi.org/10.4153/S0008439519000237
State	Published - Dec 1 2019

Scopus Subject Areas

General Mathematics

Keywords

ball-like tile
connectedness
self-affine tile

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abstract = "We construct a family of self-affine tiles in ℝd (d ≥ 2) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in ℝ2, and its extension to ℝ3 by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.",

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AU - Liu, Chuntai

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PY - 2019/12/1

Y1 - 2019/12/1

N2 - We construct a family of self-affine tiles in ℝd (d ≥ 2) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in ℝ2, and its extension to ℝ3 by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.

AB - We construct a family of self-affine tiles in ℝd (d ≥ 2) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in ℝ2, and its extension to ℝ3 by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.

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KW - connectedness

KW - self-affine tile

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Topological Properties of a Class of Higher-dimensional Self-affine Tiles

Abstract

Scopus Subject Areas

Keywords

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