The Structure of Groups with a Quasiconvex Hierarchy : : (AMS-209) / / Daniel T. Wise.
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...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2021] ©2021 |
Year of Publication: | 2021 |
Language: | English |
Series: | Annals of Mathematics Studies ;
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Physical Description: | 1 online resource (376 p.) :; 166 color illus. |
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Wise, Daniel T., author. aut http://id.loc.gov/vocabulary/relators/aut The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / Daniel T. Wise. Princeton, NJ : Princeton University Press, [2021] ©2021 1 online resource (376 p.) : 166 color illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 366 Frontmatter -- Contents -- Acknowledgments -- Chapter One Introduction -- Chapter Two CAT(0) Cube Complexes -- Chapter Three Cubical Small-Cancellation Theory -- Chapter Four Torsion and Hyperbolicity -- Chapter Five New Walls and the B(6) Condition -- Chapter Six Special Cube Complexes -- Chapter Seven Cubulations -- Chapter Eight Malnormality and Fiber-Products -- Chapter Nine Splicing Walls -- Chapter Ten Cutting X ∗ -- Chapter Eleven Hierarchies -- Chapter Twelve Virtually Special Quotient Theorem -- Chapter Thirteen Amalgams of Virtually Special Groups -- Chapter Fourteen Large Fillings Are Hyperbolic and Preservation of Quasiconvexity -- Chapter Fifteen Relatively Hyperbolic Case -- Chapter Sixteen Largeness and Omnipotence -- Chapter Seventeen Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface -- Chapter Eighteen Limit Groups and Abelian Hierarchies -- Chapter Nineteen Application Towards One-Relator Groups -- Chapter Twenty Problems -- References -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022) Group theory. Hyperbolic groups. MATHEMATICS / Group Theory. bisacsh CAT(0). Gromov. Thurston. geometric group theory. graphs of groups. hierarchies. hyperbolic groups. one relator groups. relatively hyperbolic groups. small cancellation theory. subgroup separability. virtual haken. word hyperbolic groups. Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English 9783110754001 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 9783110753776 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 English 9783110754131 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 9783110753905 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2021 9783110739121 https://doi.org/10.1515/9780691213507?locatt=mode:legacy https://www.degruyter.com/isbn/9780691213507 Cover https://www.degruyter.com/document/cover/isbn/9780691213507/original |
language |
English |
format |
eBook |
author |
Wise, Daniel T., Wise, Daniel T., |
spellingShingle |
Wise, Daniel T., Wise, Daniel T., The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Acknowledgments -- Chapter One Introduction -- Chapter Two CAT(0) Cube Complexes -- Chapter Three Cubical Small-Cancellation Theory -- Chapter Four Torsion and Hyperbolicity -- Chapter Five New Walls and the B(6) Condition -- Chapter Six Special Cube Complexes -- Chapter Seven Cubulations -- Chapter Eight Malnormality and Fiber-Products -- Chapter Nine Splicing Walls -- Chapter Ten Cutting X ∗ -- Chapter Eleven Hierarchies -- Chapter Twelve Virtually Special Quotient Theorem -- Chapter Thirteen Amalgams of Virtually Special Groups -- Chapter Fourteen Large Fillings Are Hyperbolic and Preservation of Quasiconvexity -- Chapter Fifteen Relatively Hyperbolic Case -- Chapter Sixteen Largeness and Omnipotence -- Chapter Seventeen Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface -- Chapter Eighteen Limit Groups and Abelian Hierarchies -- Chapter Nineteen Application Towards One-Relator Groups -- Chapter Twenty Problems -- References -- Index |
author_facet |
Wise, Daniel T., Wise, Daniel T., |
author_variant |
d t w dt dtw d t w dt dtw |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Wise, Daniel T., |
title |
The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / |
title_sub |
(AMS-209) / |
title_full |
The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / Daniel T. Wise. |
title_fullStr |
The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / Daniel T. Wise. |
title_full_unstemmed |
The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / Daniel T. Wise. |
title_auth |
The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / |
title_alt |
Frontmatter -- Contents -- Acknowledgments -- Chapter One Introduction -- Chapter Two CAT(0) Cube Complexes -- Chapter Three Cubical Small-Cancellation Theory -- Chapter Four Torsion and Hyperbolicity -- Chapter Five New Walls and the B(6) Condition -- Chapter Six Special Cube Complexes -- Chapter Seven Cubulations -- Chapter Eight Malnormality and Fiber-Products -- Chapter Nine Splicing Walls -- Chapter Ten Cutting X ∗ -- Chapter Eleven Hierarchies -- Chapter Twelve Virtually Special Quotient Theorem -- Chapter Thirteen Amalgams of Virtually Special Groups -- Chapter Fourteen Large Fillings Are Hyperbolic and Preservation of Quasiconvexity -- Chapter Fifteen Relatively Hyperbolic Case -- Chapter Sixteen Largeness and Omnipotence -- Chapter Seventeen Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface -- Chapter Eighteen Limit Groups and Abelian Hierarchies -- Chapter Nineteen Application Towards One-Relator Groups -- Chapter Twenty Problems -- References -- Index |
title_new |
The Structure of Groups with a Quasiconvex Hierarchy : |
title_sort |
the structure of groups with a quasiconvex hierarchy : (ams-209) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2021 |
physical |
1 online resource (376 p.) : 166 color illus. |
contents |
Frontmatter -- Contents -- Acknowledgments -- Chapter One Introduction -- Chapter Two CAT(0) Cube Complexes -- Chapter Three Cubical Small-Cancellation Theory -- Chapter Four Torsion and Hyperbolicity -- Chapter Five New Walls and the B(6) Condition -- Chapter Six Special Cube Complexes -- Chapter Seven Cubulations -- Chapter Eight Malnormality and Fiber-Products -- Chapter Nine Splicing Walls -- Chapter Ten Cutting X ∗ -- Chapter Eleven Hierarchies -- Chapter Twelve Virtually Special Quotient Theorem -- Chapter Thirteen Amalgams of Virtually Special Groups -- Chapter Fourteen Large Fillings Are Hyperbolic and Preservation of Quasiconvexity -- Chapter Fifteen Relatively Hyperbolic Case -- Chapter Sixteen Largeness and Omnipotence -- Chapter Seventeen Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface -- Chapter Eighteen Limit Groups and Abelian Hierarchies -- Chapter Nineteen Application Towards One-Relator Groups -- Chapter Twenty Problems -- References -- Index |
isbn |
9780691213507 9783110754001 9783110753776 9783110754131 9783110753905 9783110494914 9783110739121 |
url |
https://doi.org/10.1515/9780691213507?locatt=mode:legacy https://www.degruyter.com/isbn/9780691213507 https://www.degruyter.com/document/cover/isbn/9780691213507/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512/.2 |
dewey-sort |
3512 12 |
dewey-raw |
512/.2 |
dewey-search |
512/.2 |
doi_str_mv |
10.1515/9780691213507?locatt=mode:legacy |
oclc_num |
1241449093 |
work_keys_str_mv |
AT wisedanielt thestructureofgroupswithaquasiconvexhierarchyams209 AT wisedanielt structureofgroupswithaquasiconvexhierarchyams209 |
status_str |
n |
ids_txt_mv |
(DE-B1597)570994 (OCoLC)1241449093 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2021 |
is_hierarchy_title |
The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) / |
container_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English |
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