The Structure of groups with a quasiconvex hierarchy:
This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from t...
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Princeton ; Oxford
Princeton University Press
[2021]
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Schriftenreihe: | Annals of mathematics studies
Number 209 |
Schlagworte: | |
Zusammenfassung: | This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology |
Beschreibung: | x, 357 Seiten Illustrationen, Diagramme |
ISBN: | 9780691170442 |
Internformat
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245 | 1 | 0 | |a The Structure of groups with a quasiconvex hierarchy |c Daniel T. Wise |
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300 | |a x, 357 Seiten |b Illustrationen, Diagramme | ||
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338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Annals of mathematics studies |v Number 209 | |
520 | |a This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology | ||
650 | 7 | |a MATHEMATICS / Group Theory |2 bisacsh | |
650 | 4 | |a Group theory | |
650 | 4 | |a Hyperbolic groups | |
776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-691-21350-7 |
830 | 0 | |a Annals of mathematics studies |v Number 209 |w (DE-604)BV000000991 |9 209 | |
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Datensatz im Suchindex
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adam_txt | |
any_adam_object | |
any_adam_object_boolean | |
author | Wise, Daniel T. 1971- |
author_GND | (DE-588)1030054231 |
author_facet | Wise, Daniel T. 1971- |
author_role | aut |
author_sort | Wise, Daniel T. 1971- |
author_variant | d t w dt dtw |
building | Verbundindex |
bvnumber | BV047456569 |
ctrlnum | (OCoLC)1258069299 (DE-599)BVBBV047456569 |
dewey-full | 512/.2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 512 - Algebra |
dewey-raw | 512/.2 |
dewey-search | 512/.2 |
dewey-sort | 3512 12 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
discipline_str_mv | Mathematik |
format | Book |
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id | DE-604.BV047456569 |
illustrated | Illustrated |
index_date | 2024-07-03T18:04:57Z |
indexdate | 2024-07-10T09:12:39Z |
institution | BVB |
isbn | 9780691170442 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032858432 |
oclc_num | 1258069299 |
open_access_boolean | |
owner | DE-19 DE-BY-UBM |
owner_facet | DE-19 DE-BY-UBM |
physical | x, 357 Seiten Illustrationen, Diagramme |
publishDate | 2021 |
publishDateSearch | 2021 |
publishDateSort | 2021 |
publisher | Princeton University Press |
record_format | marc |
series | Annals of mathematics studies |
series2 | Annals of mathematics studies |
spelling | Wise, Daniel T. 1971- Verfasser (DE-588)1030054231 aut The Structure of groups with a quasiconvex hierarchy Daniel T. Wise Princeton ; Oxford Princeton University Press [2021] x, 357 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies Number 209 This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology MATHEMATICS / Group Theory bisacsh Group theory Hyperbolic groups Erscheint auch als Online-Ausgabe 978-0-691-21350-7 Annals of mathematics studies Number 209 (DE-604)BV000000991 209 |
spellingShingle | Wise, Daniel T. 1971- The Structure of groups with a quasiconvex hierarchy Annals of mathematics studies MATHEMATICS / Group Theory bisacsh Group theory Hyperbolic groups |
title | The Structure of groups with a quasiconvex hierarchy |
title_auth | The Structure of groups with a quasiconvex hierarchy |
title_exact_search | The Structure of groups with a quasiconvex hierarchy |
title_exact_search_txtP | The Structure of groups with a quasiconvex hierarchy |
title_full | The Structure of groups with a quasiconvex hierarchy Daniel T. Wise |
title_fullStr | The Structure of groups with a quasiconvex hierarchy Daniel T. Wise |
title_full_unstemmed | The Structure of groups with a quasiconvex hierarchy Daniel T. Wise |
title_short | The Structure of groups with a quasiconvex hierarchy |
title_sort | the structure of groups with a quasiconvex hierarchy |
topic | MATHEMATICS / Group Theory bisacsh Group theory Hyperbolic groups |
topic_facet | MATHEMATICS / Group Theory Group theory Hyperbolic groups |
volume_link | (DE-604)BV000000991 |
work_keys_str_mv | AT wisedanielt thestructureofgroupswithaquasiconvexhierarchy |