Geodesic
Embedding tiling spaces in surfaces
Charles Holton 1   ; Brian F. Martensen 2
1 Department of Mathematics The University of Texas at Austin 1 University Station//C1200 Austin, TX 78712, U.S.A.
2 Minnesota State University Wissink 273 Mankato, MN 56001, U.S.A.
Fundamenta Mathematicae, Tome 201 (2008) no. 2, pp. 99-113 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms in terms of asymptotic composants of substitutions.
DOI : 10.4064/fm201-2-1
Keywords: aperiodic minimal tiling space only finitely many asymptotic composants embeds surface only suspension symbolic interval exchange transformation possibly reversals necessary conditions aperiodic primitive substitution tiling space embed surface substitutions symbols classification nearly complete results characterize codimension hyperbolic attractors surface diffeomorphisms terms asymptotic composants substitutions

Charles Holton  1   ; Brian F. Martensen  2

1 Department of Mathematics The University of Texas at Austin 1 University Station//C1200 Austin, TX 78712, U.S.A.
2 Minnesota State University Wissink 273 Mankato, MN 56001, U.S.A. 
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Charles Holton; Brian F. Martensen. Embedding tiling spaces in surfaces. Fundamenta Mathematicae, Tome 201 (2008) no. 2, pp. 99-113. doi: 10.4064/fm201-2-1

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