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307
Finite Subdivision Rules
 Conform. Geom. Dyn
, 2001
"... . We introduce and study finite subdivision rules. A finite subdivision rule is a finite list of instructions which determines a subdivision of a given planar tiling. Given a finite subdivision rule and a planar tiling associated to it, we obtain an infinite sequence of tilings by recursively sub ..."
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Cited by 33 (8 self)
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. We introduce and study finite subdivision rules. A finite subdivision rule is a finite list of instructions which determines a subdivision of a given planar tiling. Given a finite subdivision rule and a planar tiling associated to it, we obtain an infinite sequence of tilings by recursively
SUBDIVISION RULES AND VIRTUAL ENDOMORPHISMS
"... Abstract. Suppose f: S 2 → S 2 is a postcritically finite branched covering without periodic branch points. If f is the subdivision map of a finite subdivision rule with mesh going to zero combinatorially, then the virtual endomorphism on the orbifold fundamental group associated to f is contracting ..."
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Cited by 2 (2 self)
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Abstract. Suppose f: S 2 → S 2 is a postcritically finite branched covering without periodic branch points. If f is the subdivision map of a finite subdivision rule with mesh going to zero combinatorially, then the virtual endomorphism on the orbifold fundamental group associated to f
Expansion complexes for finite subdivision rules
 I, Conform. Geom. Dyn
"... Abstract. This paper gives applications of earlier work of the authors on the use of expansion complexes for studying conformality of finite subdivision rules. The first application is that a onetile rotationally invariant finite subdivision rule (with bounded valence and mesh approaching 0) has an ..."
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Cited by 12 (5 self)
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Abstract. This paper gives applications of earlier work of the authors on the use of expansion complexes for studying conformality of finite subdivision rules. The first application is that a onetile rotationally invariant finite subdivision rule (with bounded valence and mesh approaching 0) has
MODULUS OF UNBOUNDED VALENCE SUBDIVISION RULES
"... Abstract. Cannon, Floyd and Parry have studied the modulus of finite subdivision rules extensively. We investigate the properties of the modulus of subdivision rules with linear and exponential growth at every vertex, using barycentric subdivision and a subdivision rule for the Borromean rings as ex ..."
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Abstract. Cannon, Floyd and Parry have studied the modulus of finite subdivision rules extensively. We investigate the properties of the modulus of subdivision rules with linear and exponential growth at every vertex, using barycentric subdivision and a subdivision rule for the Borromean rings
LATTÈS MAPS AND FINITE SUBDIVISION RULES
"... Abstract. This paper is concerned with realizing Lattès maps as subdivision maps of finite subdivision rules. The main result is that the Lattès maps in all but finitely many analytic conjugacy classes can be realized as subdivision maps of finite subdivision rules with one tile type. An example is ..."
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Abstract. This paper is concerned with realizing Lattès maps as subdivision maps of finite subdivision rules. The main result is that the Lattès maps in all but finitely many analytic conjugacy classes can be realized as subdivision maps of finite subdivision rules with one tile type. An example
SUBDIVISION RULES FOR SPECIAL CUBULATED GROUPS
"... Abstract. We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasiisometric information for a group. We show how these tilings detect properties such as growth, ends, divergence, etc. We inc ..."
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Abstract. We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasiisometric information for a group. We show how these tilings detect properties such as growth, ends, divergence, etc. We
CLASSIFICATION OF SUBDIVISION RULES FOR GEOMETRIC GROUPS OF LOW DIMENSION
"... Abstract. Subdivision rules create sequences of nested cell structures on CWcomplexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show that ..."
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Cited by 1 (0 self)
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Abstract. Subdivision rules create sequences of nested cell structures on CWcomplexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show
Constructing rational maps from subdivision rules
, 2003
"... Suppose R is an orientationpreserving finite subdivision rule with an edge pairing. Then the subdivision map σR is either a homeomorphism, a covering of a torus, or a critically finite branched covering of a 2sphere. If R has mesh approaching 0 and SR is a 2sphere, it is proved in Theorem 3.1 th ..."
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Cited by 14 (3 self)
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Suppose R is an orientationpreserving finite subdivision rule with an edge pairing. Then the subdivision map σR is either a homeomorphism, a covering of a torus, or a critically finite branched covering of a 2sphere. If R has mesh approaching 0 and SR is a 2sphere, it is proved in Theorem 3
CONSTRUCTING SUBDIVISION RULES FROM RATIONAL MAPS
"... Abstract. This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n the iterate f ◦n is the subdivision map of ..."
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Cited by 5 (2 self)
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Abstract. This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n the iterate f ◦n is the subdivision map
CREATING SUBDIVISION RULES FROM POLYHEDRA WITH IDENTIFICATIONS
"... Abstract. Cannon, Swenson, and others have proved numerous theorems about subdivision rules associated to hyperbolic groups with a 2sphere at infinity. However, few explicit examples are known. We construct an explicit subdivision rule for many 3manifolds from polyhedral gluings. The manifolds th ..."
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Abstract. Cannon, Swenson, and others have proved numerous theorems about subdivision rules associated to hyperbolic groups with a 2sphere at infinity. However, few explicit examples are known. We construct an explicit subdivision rule for many 3manifolds from polyhedral gluings. The manifolds
Results 1  10
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307