The structure of the rational concordance group of knots:
The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting behaviour of the Artin re...
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2007
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
885 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting behaviour of the Artin reciprocity over an infinite tower of number fields and analyzes it using tools from algebraic number theory. In higher dimensions it classifies the rational concordance group of knots whose ambient space satisfies a certain cobordism theoretic condition. In particular, he constructs infinitely many torsion elements. He shows that the structure of the rational concordance group is much more complicated than the integral concordance group from a topological viewpoint. He also investigates the structure peculiar to knots in rational homology 3-spheres. To obtain further nontrivial obstructions in this dimension, he develops a technique of controlling a certain limit of the von Neumann |
| Beschreibung: | Volume 189, number 885 (second of four numbers.) Includes bibliographical references |
| Beschreibung: | IX, 95 S. graph. Darst. |
| ISBN: | 9780821839935 |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 885 | |
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| 500 | |a Includes bibliographical references | ||
| 520 | 3 | |a The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting behaviour of the Artin reciprocity over an infinite tower of number fields and analyzes it using tools from algebraic number theory. In higher dimensions it classifies the rational concordance group of knots whose ambient space satisfies a certain cobordism theoretic condition. In particular, he constructs infinitely many torsion elements. He shows that the structure of the rational concordance group is much more complicated than the integral concordance group from a topological viewpoint. He also investigates the structure peculiar to knots in rational homology 3-spheres. To obtain further nontrivial obstructions in this dimension, he develops a technique of controlling a certain limit of the von Neumann | |
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Datensatz im Suchindex
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| adam_text | Contents
Acknowledgments ix
Chapter 1. Introduction 1
1.1. Integral and rational knot concordance 2
1.2. Main results 4
Chapter 2. Rational knots and Seifert matrices 11
2.1. Generalized Seifert surfaces 11
2.2. Limits of Seifert matrices 16
Chapter 3. Algebraic structure of Qn 21
3.1. Invariants of Seifert matrices 21
3.2. Invariants of limits of Seifert matrices 25
3.3. Computation of e(A) 31
3.4. Artin reciprocity and norm residue symbols 36
3.5. Computation of d(A) 39
Chapter 4. Geometric structure of Cn 47
4.1. Realization of rational Seifert matrices 47
4.2. Construction of slice disks in rational balls 51
4.3. Rational and integral concordance 59
4.4. Subrings of rationals 65
Chapter 5. Rational knots in dimension three 67
5.1. Rational (0) and (0.5) solvability 67
5.2. Effect of complexity change 76
5.3. Realization of Alexander modules by ribbon knots 82
5.4. Knots which are not rationally (1.5) solvable 86
Bibliography 93
vii
|
| adam_txt |
Contents
Acknowledgments ix
Chapter 1. Introduction 1
1.1. Integral and rational knot concordance 2
1.2. Main results 4
Chapter 2. Rational knots and Seifert matrices 11
2.1. Generalized Seifert surfaces 11
2.2. Limits of Seifert matrices 16
Chapter 3. Algebraic structure of Qn 21
3.1. Invariants of Seifert matrices 21
3.2. Invariants of limits of Seifert matrices 25
3.3. Computation of e(A) 31
3.4. Artin reciprocity and norm residue symbols 36
3.5. Computation of d(A) 39
Chapter 4. Geometric structure of Cn 47
4.1. Realization of rational Seifert matrices 47
4.2. Construction of slice disks in rational balls 51
4.3. Rational and integral concordance 59
4.4. Subrings of rationals 65
Chapter 5. Rational knots in dimension three 67
5.1. Rational (0) and (0.5) solvability 67
5.2. Effect of complexity change 76
5.3. Realization of Alexander modules by ribbon knots 82
5.4. Knots which are not rationally (1.5) solvable 86
Bibliography 93
vii |
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| index_date | 2024-07-02T18:31:02Z |
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| institution | BVB |
| isbn | 9780821839935 |
| language | English |
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| spelling | Cha, Jae Choon 1971- Verfasser (DE-588)17395247X aut The structure of the rational concordance group of knots Jae Choon Cha Providence, RI American Mathematical Society 2007 IX, 95 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 885 Volume 189, number 885 (second of four numbers.) Includes bibliographical references The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting behaviour of the Artin reciprocity over an infinite tower of number fields and analyzes it using tools from algebraic number theory. In higher dimensions it classifies the rational concordance group of knots whose ambient space satisfies a certain cobordism theoretic condition. In particular, he constructs infinitely many torsion elements. He shows that the structure of the rational concordance group is much more complicated than the integral concordance group from a topological viewpoint. He also investigates the structure peculiar to knots in rational homology 3-spheres. To obtain further nontrivial obstructions in this dimension, he develops a technique of controlling a certain limit of the von Neumann Knopentheorie gtt Teoria dos nós larpcal Topologia de dimensão baixa larpcal Low-dimensional topology Knot theory Concordances (Topology) Kobordismus (DE-588)4148171-9 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf PL-Topologie (DE-588)4209841-5 gnd rswk-swf Knotengruppe (DE-588)4290310-5 gnd rswk-swf S3-Problem (DE-588)4342500-8 gnd rswk-swf Niederdimensionale Topologie (DE-588)4280826-1 gnd rswk-swf Niederdimensionale Topologie (DE-588)4280826-1 s Knoten Mathematik (DE-588)4164314-8 s S3-Problem (DE-588)4342500-8 s DE-604 PL-Topologie (DE-588)4209841-5 s Kobordismus (DE-588)4148171-9 s Knotengruppe (DE-588)4290310-5 s Memoirs of the American Mathematical Society 885 (DE-604)BV008000141 885 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015957395&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cha, Jae Choon 1971- The structure of the rational concordance group of knots Memoirs of the American Mathematical Society Knopentheorie gtt Teoria dos nós larpcal Topologia de dimensão baixa larpcal Low-dimensional topology Knot theory Concordances (Topology) Kobordismus (DE-588)4148171-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd PL-Topologie (DE-588)4209841-5 gnd Knotengruppe (DE-588)4290310-5 gnd S3-Problem (DE-588)4342500-8 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd |
| subject_GND | (DE-588)4148171-9 (DE-588)4164314-8 (DE-588)4209841-5 (DE-588)4290310-5 (DE-588)4342500-8 (DE-588)4280826-1 |
| title | The structure of the rational concordance group of knots |
| title_auth | The structure of the rational concordance group of knots |
| title_exact_search | The structure of the rational concordance group of knots |
| title_exact_search_txtP | The structure of the rational concordance group of knots |
| title_full | The structure of the rational concordance group of knots Jae Choon Cha |
| title_fullStr | The structure of the rational concordance group of knots Jae Choon Cha |
| title_full_unstemmed | The structure of the rational concordance group of knots Jae Choon Cha |
| title_short | The structure of the rational concordance group of knots |
| title_sort | the structure of the rational concordance group of knots |
| topic | Knopentheorie gtt Teoria dos nós larpcal Topologia de dimensão baixa larpcal Low-dimensional topology Knot theory Concordances (Topology) Kobordismus (DE-588)4148171-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd PL-Topologie (DE-588)4209841-5 gnd Knotengruppe (DE-588)4290310-5 gnd S3-Problem (DE-588)4342500-8 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd |
| topic_facet | Knopentheorie Teoria dos nós Topologia de dimensão baixa Low-dimensional topology Knot theory Concordances (Topology) Kobordismus Knoten Mathematik PL-Topologie Knotengruppe S3-Problem Niederdimensionale Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015957395&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT chajaechoon thestructureoftherationalconcordancegroupofknots |