Topology of tiling spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2008]
|
| Schriftenreihe: | University lecture series
Volume 46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 118 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821847275 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topology of tiling spaces |c Lorenzo Sadun |
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| 264 | 4 | |c © 2008 | |
| 300 | |a X, 118 Seiten |b Illustrationen, Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a University lecture series |v Volume 46 | |
| 650 | 4 | |a Tiling spaces | |
| 650 | 4 | |a Aperiodic tilings | |
| 650 | 4 | |a Topology | |
| 650 | 4 | |a Tiling (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804138462958321664 |
|---|---|
| adam_text | Contents
Preface
Vil
Chapter
1.
Basic
notions
1
1.1.
Tilings
1
1.2.
Tiling spaces
6
1.3.
Equivalence
8
1.4.
Contructing interesting tilings
9
Chapter
2.
Tiling spaces and inverse limits
21
2.1.
Local structure
21
2.2.
Inverse limit spaces
21
2.3.
Tiling spaces are inverse limits
22
2.4. Gähler s
construction
23
2.5.
The Anderson-Putnam construction
25
Chapter
3.
Cohomology of tilings spaces
31
3.1.
Direct limits
32
3.2.
Cohomology and limits
33
3.3.
Cech
cohomology of an open cover
35
3.4.
Cofinal sets, good covers and open stars
36
3.5.
Cohomology of inverse limits
38
3.6.
Shape deformations
41
3.7.
Topological conjugacy
43
Chapter
4.
Relaxing the rules I: Rotations
45
4.1.
A new topology for tiling spaces
46
4.2.
Local structure and global topology
47
4.3.
Inverse limit structures
47
4.4.
Quotients of the tiling space
50
4.5.
Three spaces of chair tilings
50
4.6.
A flat-Earth calculation
52
4.7.
Penrose cohomology
56
Chapter
5.
Pattern-equivariant cohomology
61
5.1.
Pattern-equivariant functions
62
5.2.
How to view pattern equivariance
63
5.3.
Integer coefficients
65
5.4.
Interpreting tiling cohomology
66
vi
CONTENTS
5.5.
Gap
labeling and if-theory
67
5.6.
Averages and
Ruelle-Sullivan
currents
68
5.7.
PE cohomology and rotations
70
Chapter
6.
Tricks of the trade
75
6.1.
One dimensional methods
75
6.2.
Partial collaring
78
6.3.
Relative cohomology and eventual ranges
80
6.4.
Barge-Diamond collaring
83
6.5.
The pinwheel tiling
90
Chapter
7.
Relaxing the rules II: Tilings without finite local complexity
95
7.1.
Fault lines
95
7.2.
Analyzing a fault line
— 1
dimensional dynamics
98
7.3.
A simple 2-dimensional example
99
7.4.
The local topology of
ΩΣ
101
7.5.
Inverse limit structures
102
7.6.
A more involved example
104
7.7.
Conclusions
107
Appendix A. Solutions to selected exercises
109
Bibliography
117
|
| any_adam_object | 1 |
| author | Sadun, Lorenzo Adlai 1960- |
| author_GND | (DE-588)1159249334 |
| author_facet | Sadun, Lorenzo Adlai 1960- |
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| author_sort | Sadun, Lorenzo Adlai 1960- |
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| bvnumber | BV035206819 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 |
| ctrlnum | (OCoLC)233485421 (DE-599)BVBBV035206819 |
| dewey-full | 516/.132 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.132 |
| dewey-search | 516/.132 |
| dewey-sort | 3516 3132 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035206819 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:28:35Z |
| institution | BVB |
| isbn | 9780821847275 |
| language | English |
| lccn | 2008029389 |
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| physical | X, 118 Seiten Illustrationen, Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Sadun, Lorenzo Adlai 1960- Verfasser (DE-588)1159249334 aut Topology of tiling spaces Lorenzo Sadun Providence, Rhode Island American Mathematical Society [2008] © 2008 X, 118 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 46 Tiling spaces Aperiodic tilings Topology Tiling (Mathematics) Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Zerlegung Mathematik (DE-588)4190746-2 gnd rswk-swf Punktmenge (DE-588)4232084-7 gnd rswk-swf Punktmenge (DE-588)4232084-7 s Zerlegung Mathematik (DE-588)4190746-2 s Topologischer Raum (DE-588)4137586-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1835-9 University lecture series Volume 46 (DE-604)BV004153846 46 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017013149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sadun, Lorenzo Adlai 1960- Topology of tiling spaces University lecture series Tiling spaces Aperiodic tilings Topology Tiling (Mathematics) Topologischer Raum (DE-588)4137586-5 gnd Zerlegung Mathematik (DE-588)4190746-2 gnd Punktmenge (DE-588)4232084-7 gnd |
| subject_GND | (DE-588)4137586-5 (DE-588)4190746-2 (DE-588)4232084-7 |
| title | Topology of tiling spaces |
| title_auth | Topology of tiling spaces |
| title_exact_search | Topology of tiling spaces |
| title_full | Topology of tiling spaces Lorenzo Sadun |
| title_fullStr | Topology of tiling spaces Lorenzo Sadun |
| title_full_unstemmed | Topology of tiling spaces Lorenzo Sadun |
| title_short | Topology of tiling spaces |
| title_sort | topology of tiling spaces |
| topic | Tiling spaces Aperiodic tilings Topology Tiling (Mathematics) Topologischer Raum (DE-588)4137586-5 gnd Zerlegung Mathematik (DE-588)4190746-2 gnd Punktmenge (DE-588)4232084-7 gnd |
| topic_facet | Tiling spaces Aperiodic tilings Topology Tiling (Mathematics) Topologischer Raum Zerlegung Mathematik Punktmenge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017013149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT sadunlorenzoadlai topologyoftilingspaces |