Topological properties of a class of self-affine tiles in R3

Guotai Deng; Chuntai Liu; Sze Man Ngai

doi:10.1090/tran/7055

Topological properties of a class of self-affine tiles in R³

Guotai Deng, Chuntai Liu, Sze Man Ngai

Mathematical Sciences

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

11 Scopus citations

Abstract

We construct a class of connected self-affine tiles in R³ and prove that it contains a subclass of tiles that are homeomorphic to a unit ball in R³. Our construction is obtained by generalizing a two-dimensional one by Deng and Lau. The proof of ball-likeness is inspired by the construction of a homeomorphism from Alexander’s horned ball to a 3-ball.

Original language	English
Pages (from-to)	1321-1350
Number of pages	30
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	2
DOIs	https://doi.org/10.1090/tran/7055
State	Published - Feb 2018

Keywords

Ball-like tiles
Connectedness
Self-affine tile

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10.1090/tran/7055

Cite this

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abstract = "We construct a class of connected self-affine tiles in R3 and prove that it contains a subclass of tiles that are homeomorphic to a unit ball in R3. Our construction is obtained by generalizing a two-dimensional one by Deng and Lau. The proof of ball-likeness is inspired by the construction of a homeomorphism from Alexander{\textquoteright}s horned ball to a 3-ball.",

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KW - Self-affine tile

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Topological properties of a class of self-affine tiles in R³

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Keywords

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