Groups acting on graphs:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
1989
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge Studies in Advanced Mathematics
17 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 283 Seiten Illustrationen |
| ISBN: | 0521230330 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV001384661 | ||
| 003 | DE-604 | ||
| 005 | 20210315 | ||
| 007 | t | ||
| 008 | 890713s1989 a||| |||| 00||| eng d | ||
| 020 | |a 0521230330 |9 0-521-23033-0 | ||
| 035 | |a (OCoLC)246865802 | ||
| 035 | |a (DE-599)BVBBV001384661 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91G |a DE-384 |a DE-703 |a DE-739 |a DE-355 |a DE-824 |a DE-29T |a DE-20 |a DE-83 |a DE-11 |a DE-188 |a DE-19 | ||
| 082 | 0 | |a 512.2222 | |
| 084 | |a SK 260 |0 (DE-625)143227: |2 rvk | ||
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a 20F32 |2 msc | ||
| 084 | |a 05C25 |2 msc | ||
| 084 | |a MAT 055f |2 stub | ||
| 084 | |a MAT 200f |2 stub | ||
| 100 | 1 | |a Dicks, Warren |d 1947- |e Verfasser |0 (DE-588)172043336 |4 aut | |
| 245 | 1 | 0 | |a Groups acting on graphs |c Warren Dicks, Professor in mathematics, Universitat Autònoma de Barcelona, M. J. Dunwoody, reader in mathematics, University of Sussex |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 1989 | |
| 300 | |a XVI, 283 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge Studies in Advanced Mathematics |v 17 | |
| 650 | 4 | |a Gruppentheorie - Graphentheorie - Homologische Algebra | |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | 1 | |a Gruppentheorie |0 (DE-588)4072157-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Dunwoody, M. J. |e Verfasser |4 aut | |
| 830 | 0 | |a Cambridge Studies in Advanced Mathematics |v 17 |w (DE-604)BV000003678 |9 17 | |
| 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=000846338&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-000846338 | ||
Datensatz im Suchindex
| _version_ | 1804115790289436672 |
|---|---|
| adam_text | Contents
Preface xi
Conventions xv
I Groups and graphs 1
1 Groups 1
2 Graphs 4
3 Graphs of groups 11
4 Groups acting on trees 15
5 Trees for certain automorphism groups 21
6 The exact sequence for a tree 28
7 The fundamental group and its tree 31
8 Free groups 36
9 Groups acting on connected graphs 39
10 Free products 42
Notes and comments 45
11 Cutting graphs and building trees 47
1 Tree sets 47
2 The Boolean ring of a graph 54
3 Distance transitive graphs 67
Notes and comments 71
III The Almost Stability Theorem 73
1 Motivation 73
2 Digression: the classical approach 74
3 Blowing up 78
4 Notation 80
5 Preliminaries 82
vii
viii Contents
6 The main argument 83
7 Finitely generated extensions 90
8 The general case 95
Notes and comments 100
IV Applications of the Almost Stability Theorem 101
1 Subgroups of finite index 101
2 Derivations to projective modules 107
3 Cohomological dimension one 110
4 Projective augmentation modules 115
5 Splitting augmentation ideals 120
6 Ends of groups 124
7 Accessibility 130
Notes and comments 133
V Poincare duality 135
1 Introduction 135
2 PD modules 141
3 PD groups 155
4 Low dimensional examples 159
5 Subgroups of finite index 170
6 Subgroups of infinite index 173
7 PD pairs 175
8 Trees and Poincare duality 183
9 Relative ends 192
10 PD2 pairs 200
11 Projective modules over group rings 202
12 PD2 groups 207
Notes and comments 213
VI Two dimensional complexes and three dimensional
manifolds 215
1 Simplicial complexes 215
2 Orbit spaces 220
3 Patterns and tracks 223
4 Almost finitely presented groups 229
5 Addition of patterns 233
6 The accessibility of almost finitely presented groups 242
7 Two manifolds 243
8 Patterns and surfaces in three manifolds 246
Contents ix
9 Simplifying surface maps 249
10 The equivariant sphere and loop theorems 255
11 The Loop Theorem 263
12 The Sphere Theorem 268
Notes and comments 271
Bibliography and author index 272
Symbol index 276
Subject index 279
|
| any_adam_object | 1 |
| author | Dicks, Warren 1947- Dunwoody, M. J. |
| author_GND | (DE-588)172043336 |
| author_facet | Dicks, Warren 1947- Dunwoody, M. J. |
| author_role | aut aut |
| author_sort | Dicks, Warren 1947- |
| author_variant | w d wd m j d mj mjd |
| building | Verbundindex |
| bvnumber | BV001384661 |
| classification_rvk | SK 260 SK 890 |
| classification_tum | MAT 055f MAT 200f |
| ctrlnum | (OCoLC)246865802 (DE-599)BVBBV001384661 |
| dewey-full | 512.2222 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2222 |
| dewey-search | 512.2222 |
| dewey-sort | 3512.2222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01982nam a2200469 cb4500</leader><controlfield tag="001">BV001384661</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210315 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890713s1989 a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521230330</subfield><subfield code="9">0-521-23033-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246865802</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV001384661</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.2222</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 260</subfield><subfield code="0">(DE-625)143227:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">20F32</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">05C25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 055f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 200f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dicks, Warren</subfield><subfield code="d">1947-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)172043336</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Groups acting on graphs</subfield><subfield code="c">Warren Dicks, Professor in mathematics, Universitat Autònoma de Barcelona, M. J. Dunwoody, reader in mathematics, University of Sussex</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 283 Seiten</subfield><subfield code="b">Illustrationen</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">Cambridge Studies in Advanced Mathematics</subfield><subfield code="v">17</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gruppentheorie - Graphentheorie - Homologische Algebra</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dunwoody, M. J.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge Studies in Advanced Mathematics</subfield><subfield code="v">17</subfield><subfield code="w">(DE-604)BV000003678</subfield><subfield code="9">17</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=000846338&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:BVB01-000846338</subfield></datafield></record></collection> |
| id | DE-604.BV001384661 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:28:12Z |
| institution | BVB |
| isbn | 0521230330 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000846338 |
| oclc_num | 246865802 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-83 DE-11 DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-83 DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | XVI, 283 Seiten Illustrationen |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge Studies in Advanced Mathematics |
| series2 | Cambridge Studies in Advanced Mathematics |
| spelling | Dicks, Warren 1947- Verfasser (DE-588)172043336 aut Groups acting on graphs Warren Dicks, Professor in mathematics, Universitat Autònoma de Barcelona, M. J. Dunwoody, reader in mathematics, University of Sussex 1. publ. Cambridge [u.a.] Cambridge University Press 1989 XVI, 283 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Cambridge Studies in Advanced Mathematics 17 Gruppentheorie - Graphentheorie - Homologische Algebra Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Gruppentheorie (DE-588)4072157-7 s DE-604 Dunwoody, M. J. Verfasser aut Cambridge Studies in Advanced Mathematics 17 (DE-604)BV000003678 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000846338&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dicks, Warren 1947- Dunwoody, M. J. Groups acting on graphs Cambridge Studies in Advanced Mathematics Gruppentheorie - Graphentheorie - Homologische Algebra Gruppentheorie (DE-588)4072157-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4113782-6 |
| title | Groups acting on graphs |
| title_auth | Groups acting on graphs |
| title_exact_search | Groups acting on graphs |
| title_full | Groups acting on graphs Warren Dicks, Professor in mathematics, Universitat Autònoma de Barcelona, M. J. Dunwoody, reader in mathematics, University of Sussex |
| title_fullStr | Groups acting on graphs Warren Dicks, Professor in mathematics, Universitat Autònoma de Barcelona, M. J. Dunwoody, reader in mathematics, University of Sussex |
| title_full_unstemmed | Groups acting on graphs Warren Dicks, Professor in mathematics, Universitat Autònoma de Barcelona, M. J. Dunwoody, reader in mathematics, University of Sussex |
| title_short | Groups acting on graphs |
| title_sort | groups acting on graphs |
| topic | Gruppentheorie - Graphentheorie - Homologische Algebra Gruppentheorie (DE-588)4072157-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Gruppentheorie - Graphentheorie - Homologische Algebra Gruppentheorie Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000846338&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT dickswarren groupsactingongraphs AT dunwoodymj groupsactingongraphs |