Topological Properties of a Class of Self-Affine Tiles in R³

Authors

Guotai Deng, Central China Normal UniversityFollow
Chuntai Liu, Wuhan Polytechnic UniversityFollow
Sze-Man Ngai, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2-2018

Publication Title

Transactions of the American Mathematical Society

DOI

10.1090/tran/7055

ISSN

1088-6850

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.

Recommended Citation

Deng, Guotai, Chuntai Liu, Sze-Man Ngai. 2018. "Topological Properties of a Class of Self-Affine Tiles in R³." Transactions of the American Mathematical Society, 370 (2): 1321-1350. doi: 10.1090/tran/7055
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/650