Volume 17, issue 3 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Pattern-equivariant homology

James J Walton

Algebraic & Geometric Topology 17 (2017) 1323–1373
Bibliography
1 J E Anderson, I F Putnam, Topological invariants for substitution tilings and their associated C–algebras, Ergodic Theory Dynam. Systems 18 (1998) 509 MR1631708
2 P Arnoux, V Berthé, H Ei, S Ito, Tilings, quasicrystals, discrete planes, generalized substitutions, and multidimensional continued fractions, from: "Discrete models: combinatorics, computation, and geometry", Discrete Math. Theor. Comput. Sci. Proc. AA, Maison Inform. Math. Discrèt. (2001) 59 MR1888763
3 P Arnoux, G Rauzy, Représentation géométrique de suites de complexité 2n + 1, Bull. Soc. Math. France 119 (1991) 199 MR1116845
4 M Baake, M Schlottmann, P D Jarvis, Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability, J. Phys. A 24 (1991) 4637 MR1132337
5 M Barge, B Diamond, J Hunton, L Sadun, Cohomology of substitution tiling spaces, Ergodic Theory Dynam. Systems 30 (2010) 1607 MR2736888
6 J Bellissard, A Julien, J Savinien, Tiling groupoids and Bratteli diagrams, Ann. Henri Poincaré 11 (2010) 69 MR2658985
7 R Berger, The undecidability of the domino problem, 66, Amer. Math. Soc. (1966) 72 MR0216954
8 V Berthé, A Siegel, Tilings associated with beta-numeration and substitutions, Integers 5 (2005) MR2191748
9 A Björner, Posets, regular CW complexes and Bruhat order, European J. Combin. 5 (1984) 7 MR746039
10 R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
11 P L Bowers, K Stephenson, A “regular” pentagonal tiling of the plane, Conform. Geom. Dyn. 1 (1997) 58 MR1479069
12 A Clark, J Hunton, Tiling spaces, codimension one attractors and shape, New York J. Math. 18 (2012) 765 MR2991423
13 A Clark, L Sadun, When shape matters: deformations of tiling spaces, Ergodic Theory Dynam. Systems 26 (2006) 69 MR2201938
14 F Durand, Linearly recurrent subshifts have a finite number of non-periodic subshift factors, Ergodic Theory Dynam. Systems 20 (2000) 1061 MR1779393
15 A Forrest, J Hunton, J Kellendonk, Topological invariants for projection method patterns, 758, Amer. Math. Soc. (2002) MR1922206
16 N P Frank, A primer of substitution tilings of the Euclidean plane, Expo. Math. 26 (2008) 295 MR2462439
17 N P Frank, L Sadun, Fusion : a general framework for hierarchical tilings of d, Geom. Dedicata 171 (2014) 149 MR3226791
18 F Gähler, G R Maloney, Cohomology of one-dimensional mixed substitution tiling spaces, Topology Appl. 160 (2013) 703 MR3022738
19 D Gonçalves, On the K–theory of the stable C–algebras from substitution tilings, J. Funct. Anal. 260 (2011) 998 MR2747010
20 B Grünbaum, G C Shephard, Tilings and patterns, W H Freeman (1987) MR857454
21 A Haynes, M Kelly, B Weiss, Equivalence relations on separated nets arising from linear toral flows, Proc. Lond. Math. Soc. 109 (2014) 1203 MR3283615
22 A Haynes, H Koivusalo, J Walton, A characterization of linearly repetitive cut and project sets, preprint (2015) arXiv:1503.04091
23 J Kellendonk, The local structure of tilings and their integer group of coinvariants, Comm. Math. Phys. 187 (1997) 115 MR1463824
24 J Kellendonk, Pattern-equivariant functions and cohomology, J. Phys. A 36 (2003) 5765 MR1985494
25 J Kellendonk, Pattern equivariant functions, deformations and equivalence of tiling spaces, Ergodic Theory Dynam. Systems 28 (2008) 1153 MR2437225
26 J Kellendonk, M V Lawson, Tiling semigroups, J. Algebra 224 (2000) 140 MR1736698
27 J Kellendonk, I F Putnam, Tilings, C–algebras, and K–theory, from: "Directions in mathematical quasicrystals" (editors M Baake, R V Moody), CRM Monogr. Ser. 13, Amer. Math. Soc. (2000) 177 MR1798993
28 J Kellendonk, I F Putnam, The Ruelle–Sullivan map for actions of n, Math. Ann. 334 (2006) 693 MR2207880
29 M Kelly, L Sadun, Pattern equivariant cohomology and theorems of Kesten and Oren, Bull. Lond. Math. Soc. 47 (2015) 13 MR3312959
30 G Lafitte, M Weiss, Computability of tilings, from: "Fifth International Conference on Theoretical Computer Science" (editors G Ausiello, J Karhumäki, G Mauri, L Ong), Int. Fed. Inf. Process. 273, Springer (2008) 187 MR2757375
31 J R Munkres, Elements of algebraic topology, Addison-Wesley (1984) MR755006
32 N Ormes, C Radin, L Sadun, A homeomorphism invariant for substitution tiling spaces, Geom. Dedicata 90 (2002) 153 MR1898159
33 R Penrose, Pentaplexity: a class of nonperiodic tilings of the plane, from: "Geometrical combinatorics" (editors F C Holroyd, R J Wilson), Res. Notes in Math. 114, Pitman (1984) 55 MR777156
34 N Priebe Frank, L Sadun, Fusion tilings with infinite local complexity, Topology Proc. 43 (2014) 235 MR3104922
35 C Radin, Aperiodic tilings, ergodic theory, and rotations, from: "The mathematics of long-range aperiodic order" (editor R V Moody), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 489, Kluwer (1997) 499 MR1460035
36 D Rust, An uncountable set of tiling spaces with distinct cohomology, Topology Appl. 205 (2016) 58 MR3493307
37 L Sadun, Pattern-equivariant cohomology with integer coefficients, Ergodic Theory Dynam. Systems 27 (2007) 1991 MR2371606
38 L Sadun, Topology of tiling spaces, 46, Amer. Math. Soc. (2008) MR2446623
39 L Sadun, R F Williams, Tiling spaces are Cantor set fiber bundles, Ergodic Theory Dynam. Systems 23 (2003) 307 MR1971208
40 K Schmidt, Multi-dimensional symbolic dynamical systems, from: "Codes, systems, and graphical models" (editors B Marcus, J Rosenthal), IMA Vol. Math. Appl. 123, Springer (2001) 67 MR1861953
41 D Shechtman, I Blech, D Gratias, J W Cahn, Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 53 (1984) 1951
42 J Walton, Cohomology of rotational tiling spaces, preprint (2016) arXiv:1609.06606
43 E C Zeeman, Dihomology, III : A generalization of the Poincaré duality for manifolds, Proc. London Math. Soc. 13 (1963) 155 MR0153011