Bounded cohomology and geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Bonn
Math. Inst. der Univ.
2004
|
| Series: | Bonner mathematische Schriften
368 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 126 S. |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV021272556 | ||
| 003 | DE-604 | ||
| 005 | 20070822 | ||
| 007 | t | ||
| 008 | 051221s2004 m||| 00||| eng d | ||
| 035 | |a (OCoLC)62768224 | ||
| 035 | |a (DE-599)BVBBV021272556 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-703 |a DE-20 |a DE-91G |a DE-706 |a DE-19 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA1 | |
| 084 | |a SI 180 |0 (DE-625)143093: |2 rvk | ||
| 100 | 1 | |a Wienhard, Anna Katharina |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bounded cohomology and geometry |c vorgelegt von Anna Katharina Wienhard |
| 264 | 1 | |a Bonn |b Math. Inst. der Univ. |c 2004 | |
| 300 | |a 126 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Bonner mathematische Schriften |v 368 | |
| 502 | |a Bonn, Univ., Diss., 2004 | ||
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Symmetric spaces | |
| 650 | 0 | 7 | |a Hermitescher Raum |0 (DE-588)4159618-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kohomologie |0 (DE-588)4031700-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Beschränktheit |g Mathematik |0 (DE-588)4289271-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrie |0 (DE-588)4020236-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Kohomologie |0 (DE-588)4031700-6 |D s |
| 689 | 0 | 1 | |a Beschränktheit |g Mathematik |0 (DE-588)4289271-5 |D s |
| 689 | 0 | 2 | |a Geometrie |0 (DE-588)4020236-7 |D s |
| 689 | 0 | 3 | |a Hermitescher Raum |0 (DE-588)4159618-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Bonner mathematische Schriften |v 368 |w (DE-604)BV000001610 |9 368 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014593654&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014593654 | ||
Record in the Search Index
| _version_ | 1804135053109755904 |
|---|---|
| adam_text | Titel: Bounded cohomology and geometry
Autor: Wienhard, Anna Katharina
Jahr: 2004
Contents
Preface and Acknowledgement 5
Introduction 7
Chapter 1. A short introduction to bounded cohomology 15
1. The definition 15
2. Functorial approach 17
3. Implementing pull-back maps 20
4. Properties 22
Chapter 2. Symmetric spaces 23
1. Definitions 23
2. Boundaries 26
3. Totally geodesic submanifolds 27
4. Real structure and duality 28
Chapter 3. Hermitian symmetric spaces 29
1. Definitions 29
2. The Borel embedding 30
3. The Harish-Chandra embedding 31
4. Two classes: tube type and not 35
5. Examples 36
Chapter 4. The Shilov boundary 45
1. A homeomorphism of boundaries 45
2. The Shilov boundary as homogeneous space 46
3. The Bruhat decomposition 46
4. The space of triples of pairwise transverse points 48
5. A complex model for the Shilov boundary 50
6. Parametrizing the Shilov boundary of a tube type domain 51
Exkurs: A generalized Maslov index 55
The classical Maslov index 55
The Maslov cycle in the general case 55
Chapter 5. Cocycles 57
1. The Bergmann and the Kafaler cocycle 57
2. The Kahler cocycle as bounded cohomology class 60
3. The Bergmann cocycle as bounded cohomology class 60
4. The Hermitian triple product 60
5. A generalized Maslov cocycle for tube type domains 62
Chapter 6. Tight homomorphisms and embeddings 67
1. Definition and properties of o tight homomorphisms 67
2. Kahler tight homomorphisms 68
3. Tight embeddings and their properties 70
4. The Kahler form on Lie algebra level 73
5. Classification of tight embeddings 77
6. Open questions 82
Chapter 7. Group actions on Hermitian symmetric spaces 85
1. Zariski dense representations 85
2. Limit sets in the Shilov boundary 88
3. Structure of the representation variety 89
Chapter 8. Representations of surface groups 93
1. The Toledo invariant 93
2. Maximal representations 95
3. Weakly maximal representations with Zariski dense image 96
4. Characterizing maximal representations 103
5. The maximal part of the representation variety 108
6. Anosov flows 110
Appendix 119
Some facts about Lie groups and Lie algebras 119
Some facts about Jordan algebras 121
Bibliography 123
|
| adam_txt |
Titel: Bounded cohomology and geometry
Autor: Wienhard, Anna Katharina
Jahr: 2004
Contents
Preface and Acknowledgement 5
Introduction 7
Chapter 1. A short introduction to bounded cohomology 15
1. The definition 15
2. Functorial approach 17
3. Implementing pull-back maps 20
4. Properties 22
Chapter 2. Symmetric spaces 23
1. Definitions 23
2. Boundaries 26
3. Totally geodesic submanifolds 27
4. Real structure and duality 28
Chapter 3. Hermitian symmetric spaces 29
1. Definitions 29
2. The Borel embedding 30
3. The Harish-Chandra embedding 31
4. Two classes: tube type and not 35
5. Examples 36
Chapter 4. The Shilov boundary 45
1. A homeomorphism of boundaries 45
2. The Shilov boundary as homogeneous space 46
3. The Bruhat decomposition 46
4. The space of triples of pairwise transverse points 48
5. A complex model for the Shilov boundary 50
6. Parametrizing the Shilov boundary of a tube type domain 51
Exkurs: A generalized Maslov index 55
The classical Maslov index 55
The Maslov cycle in the general case 55
Chapter 5. Cocycles 57
1. The Bergmann and the Kafaler cocycle 57
2. The Kahler cocycle as bounded cohomology class 60
3. The Bergmann cocycle as bounded cohomology class 60
4. The Hermitian triple product 60
5. A generalized Maslov cocycle for tube type domains 62
Chapter 6. Tight homomorphisms and embeddings 67
1. Definition and properties of o tight homomorphisms 67
2. Kahler tight homomorphisms 68
3. Tight embeddings and their properties 70
4. The Kahler form on Lie algebra level 73
5. Classification of tight embeddings 77
6. Open questions 82
Chapter 7. Group actions on Hermitian symmetric spaces 85
1. Zariski dense representations 85
2. Limit sets in the Shilov boundary 88
3. Structure of the representation variety 89
Chapter 8. Representations of surface groups 93
1. The Toledo invariant 93
2. Maximal representations 95
3. Weakly maximal representations with Zariski dense image 96
4. Characterizing maximal representations 103
5. The maximal part of the representation variety 108
6. Anosov flows 110
Appendix 119
Some facts about Lie groups and Lie algebras 119
Some facts about Jordan algebras 121
Bibliography 123 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Wienhard, Anna Katharina |
| author_facet | Wienhard, Anna Katharina |
| author_role | aut |
| author_sort | Wienhard, Anna Katharina |
| author_variant | a k w ak akw |
| building | Verbundindex |
| bvnumber | BV021272556 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 |
| callnumber-search | QA1 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 180 |
| ctrlnum | (OCoLC)62768224 (DE-599)BVBBV021272556 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01850nam a2200457 cb4500</leader><controlfield tag="001">BV021272556</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20070822 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">051221s2004 m||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)62768224</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021272556</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA1</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 180</subfield><subfield code="0">(DE-625)143093:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wienhard, Anna Katharina</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bounded cohomology and geometry</subfield><subfield code="c">vorgelegt von Anna Katharina Wienhard</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Bonn</subfield><subfield code="b">Math. Inst. der Univ.</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">126 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Bonner mathematische Schriften</subfield><subfield code="v">368</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">Bonn, Univ., Diss., 2004</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Homology theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetric spaces</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hermitescher Raum</subfield><subfield code="0">(DE-588)4159618-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kohomologie</subfield><subfield code="0">(DE-588)4031700-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Beschränktheit</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4289271-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kohomologie</subfield><subfield code="0">(DE-588)4031700-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Beschränktheit</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4289271-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Hermitescher Raum</subfield><subfield code="0">(DE-588)4159618-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Bonner mathematische Schriften</subfield><subfield code="v">368</subfield><subfield code="w">(DE-604)BV000001610</subfield><subfield code="9">368</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014593654&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-014593654</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV021272556 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:44:56Z |
| indexdate | 2024-07-09T20:34:23Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014593654 |
| oclc_num | 62768224 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-20 DE-91G DE-BY-TUM DE-706 DE-19 DE-BY-UBM DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-20 DE-91G DE-BY-TUM DE-706 DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | 126 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Math. Inst. der Univ. |
| record_format | marc |
| series | Bonner mathematische Schriften |
| series2 | Bonner mathematische Schriften |
| spelling | Wienhard, Anna Katharina Verfasser aut Bounded cohomology and geometry vorgelegt von Anna Katharina Wienhard Bonn Math. Inst. der Univ. 2004 126 S. txt rdacontent n rdamedia nc rdacarrier Bonner mathematische Schriften 368 Bonn, Univ., Diss., 2004 Homology theory Symmetric spaces Hermitescher Raum (DE-588)4159618-3 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Beschränktheit Mathematik (DE-588)4289271-5 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kohomologie (DE-588)4031700-6 s Beschränktheit Mathematik (DE-588)4289271-5 s Geometrie (DE-588)4020236-7 s Hermitescher Raum (DE-588)4159618-3 s DE-604 Bonner mathematische Schriften 368 (DE-604)BV000001610 368 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014593654&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wienhard, Anna Katharina Bounded cohomology and geometry Bonner mathematische Schriften Homology theory Symmetric spaces Hermitescher Raum (DE-588)4159618-3 gnd Kohomologie (DE-588)4031700-6 gnd Beschränktheit Mathematik (DE-588)4289271-5 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4159618-3 (DE-588)4031700-6 (DE-588)4289271-5 (DE-588)4020236-7 (DE-588)4113937-9 |
| title | Bounded cohomology and geometry |
| title_auth | Bounded cohomology and geometry |
| title_exact_search | Bounded cohomology and geometry |
| title_exact_search_txtP | Bounded cohomology and geometry |
| title_full | Bounded cohomology and geometry vorgelegt von Anna Katharina Wienhard |
| title_fullStr | Bounded cohomology and geometry vorgelegt von Anna Katharina Wienhard |
| title_full_unstemmed | Bounded cohomology and geometry vorgelegt von Anna Katharina Wienhard |
| title_short | Bounded cohomology and geometry |
| title_sort | bounded cohomology and geometry |
| topic | Homology theory Symmetric spaces Hermitescher Raum (DE-588)4159618-3 gnd Kohomologie (DE-588)4031700-6 gnd Beschränktheit Mathematik (DE-588)4289271-5 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Homology theory Symmetric spaces Hermitescher Raum Kohomologie Beschränktheit Mathematik Geometrie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014593654&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001610 |
| work_keys_str_mv | AT wienhardannakatharina boundedcohomologyandgeometry |