Ordered groups and topology:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2016]
|
| Series: | Graduate studies in mathematics
176 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | x, 154 Diagramme |
| ISBN: | 9781470431068 |
Staff View
MARC
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| 650 | 4 | |a Ordered groups | |
| 650 | 4 | |a Topology | |
| 650 | 4 | |a Low-dimensional topology | |
| 650 | 4 | |a Knot theory | |
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| 650 | 4 | |a Manifolds and cell complexes ... Research exposition (monographs, survey articles) | |
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Record in the Search Index
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| adam_text | Titel: Ordered groups and topology
Autor: Clay, Adam
Jahr: 2016
I Contents Preface ix Chapter 1. Orderable groups and their algebraic properties §1.1. Invariant orderings §1.2. Examples §1.3. Bi-orderable groups §1.4. Positive cone §1.5. Topology and the spaces of orderings §1.6. Testing for orderability §1.7. Characterization of left-orderable groups §1.8. Group rings and zero divisors §1.9. Torsion-free groups which are not left-orderable Chapter 2. Holder’s theorem, convex subgroups and dynamics §2.1. Holder’s theorem §2.2. Convex subgroups §2.3. Bi-orderable groups are locally indicable §2.4. The dynamic realization of a left-ordering Chapter 3. Free groups, surface groups and covering spaces §3.1. Surfaces §3.2. Ordering free groups §3.3. Ordering surface groups §3.4. A theorem of Farrell 1 2 3 6 7 8 11 13 15 16 21 21 24 26 27 31 31 33 36 39 v
VI Contents Chapter 4. Knots §4.1. Review of classical knot theory §4.2. The Wirtinger presentation §4.3. Knot groups are locally indicable §4.4. Bi-ordering certain knot groups §4.5. Crossing changes: A theorem of Smythe Chapter 5. Three-dimensional manifolds §5.1. Ordering 3-manifold groups §5.2. Surgery §5.3. Branched coverings §5.4. Bi-orderability and surgery Chapter 6. Foliations §6.1. Examples §6.2. The leaf space §6.3. Seifert fibered spaces §6.4. M-covered foliations §6.5. The universal circle Chapter 7. Left-orderings of the braid groups §7.1. Order ability properties of the braid groups §7.2. The Dehornoy ordering of B n §7.3. Thurston’s orderings of B n §7.4. Applications of the Dehornoy ordering to knot theory Chapter § 8 . 1 . § 8 . 2 . §8.3. §8.4. §8.5. 8. Groups of homeomorphisms Homeomorphisms of a space PL homeomorphisms of the cube Proof of Theorem 8.6 Generalizations Homeomorphisms of the cube Chapter 9. Conradian left-orderings and local indicability §9.1. The defining property of a Conradian ordering §9.2. Characterizations of Conradian left-order ability 43 43 47 49 51 60 65 66 67 71 75 77 77 81 81 87 89 91 93 95 97 108 115 115 116 118 119 120 121 122 126
Contents vii Chapter 10. Spaces of orderings) 131 §10.1. The natural actions on LO(G) 132 §10.2. Orderings of Z n and Sikora’s theorem 133 §10.3. Examples of groups without isolated orderings 135 §10.4. The space of orderings of a free product 137 §10.5. Examples of groups with isolated orderings 139 §10.6. The number of orderings of a group 140 §10.7. Recurrent orderings and a theorem of Witte-Morris 144 Bibliography 147 Index 153
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| dewey-search | 512/.55 |
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| indexdate | 2024-07-10T07:37:53Z |
| institution | BVB |
| isbn | 9781470431068 |
| language | English |
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| physical | x, 154 Diagramme |
| publishDate | 2016 |
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| publisher | American Mathematical Society |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Clay, Adam 1981- Verfasser (DE-588)112427376X aut Ordered groups and topology Adam Clay, Dale Rolfsen Providence, Rhode Island American Mathematical Society [2016] © 2016 x, 154 Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 176 Includes bibliographical references and index Manifolds and cell complexes ... Research exposition (monographs, survey articles) msc Group theory and generalizations ... Special aspects of infinite or finite groups ... Ordered groups msc Manifolds and cell complexes ... Low-dimensional topology ... Topological methods in group theory msc Ordered groups Topology Low-dimensional topology Knot theory Manifolds (Mathematics) Manifolds and cell complexes ... Research exposition (monographs, survey articles) Group theory and generalizations ... Special aspects of infinite or finite groups ... Ordered groups Manifolds and cell complexes ... Low-dimensional topology ... Topological methods in group theory Rolfsen, Dale 1942- Verfasser (DE-588)1319301045 aut Graduate studies in mathematics 176 (DE-604)BV009739289 176 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029306047&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Clay, Adam 1981- Rolfsen, Dale 1942- Ordered groups and topology Graduate studies in mathematics Manifolds and cell complexes ... Research exposition (monographs, survey articles) msc Group theory and generalizations ... Special aspects of infinite or finite groups ... Ordered groups msc Manifolds and cell complexes ... Low-dimensional topology ... Topological methods in group theory msc Ordered groups Topology Low-dimensional topology Knot theory Manifolds (Mathematics) Manifolds and cell complexes ... Research exposition (monographs, survey articles) Group theory and generalizations ... Special aspects of infinite or finite groups ... Ordered groups Manifolds and cell complexes ... Low-dimensional topology ... Topological methods in group theory |
| title | Ordered groups and topology |
| title_auth | Ordered groups and topology |
| title_exact_search | Ordered groups and topology |
| title_full | Ordered groups and topology Adam Clay, Dale Rolfsen |
| title_fullStr | Ordered groups and topology Adam Clay, Dale Rolfsen |
| title_full_unstemmed | Ordered groups and topology Adam Clay, Dale Rolfsen |
| title_short | Ordered groups and topology |
| title_sort | ordered groups and topology |
| topic | Manifolds and cell complexes ... Research exposition (monographs, survey articles) msc Group theory and generalizations ... Special aspects of infinite or finite groups ... Ordered groups msc Manifolds and cell complexes ... Low-dimensional topology ... Topological methods in group theory msc Ordered groups Topology Low-dimensional topology Knot theory Manifolds (Mathematics) Manifolds and cell complexes ... Research exposition (monographs, survey articles) Group theory and generalizations ... Special aspects of infinite or finite groups ... Ordered groups Manifolds and cell complexes ... Low-dimensional topology ... Topological methods in group theory |
| topic_facet | Manifolds and cell complexes ... Research exposition (monographs, survey articles) Group theory and generalizations ... Special aspects of infinite or finite groups ... Ordered groups Manifolds and cell complexes ... Low-dimensional topology ... Topological methods in group theory Ordered groups Topology Low-dimensional topology Knot theory Manifolds (Mathematics) |
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