LEADER 04104nam 2200673 450 001 9910554261903321 005 20230630001139.0 010 $a0-691-21350-X 024 7 $a10.1515/9780691213507 035 $a(CKB)4100000011807718 035 $a(DE-B1597)570994 035 $a(DE-B1597)9780691213507 035 $a(MiAaPQ)EBC6512276 035 $a(Au-PeEL)EBL6512276 035 $a(OCoLC)1241449093 035 $a(EXLCZ)994100000011807718 100 $a20211007d2021 uy 0 101 0 $aeng 135 $aur||#|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe structure of groups with a quasiconvex hierarchy /$fDaniel T. Wise 210 1$aPrinceton, New Jersey :$cPrinceton University Press,$d[2021] 210 4$dİ2021 215 $a1 online resource (376 p.) $c166 color illus 225 0 $aAnnals of Mathematics Studies ;$v396 311 $a0-691-17045-2 311 $a0-691-17044-4 320 $aIncludes bibliographical references and index. 327 $tFrontmatter --$tContents --$tAcknowledgments --$tChapter One Introduction --$tChapter Two CAT(0) Cube Complexes --$tChapter Three Cubical Small-Cancellation Theory --$tChapter Four Torsion and Hyperbolicity --$tChapter Five New Walls and the B(6) Condition --$tChapter Six Special Cube Complexes --$tChapter Seven Cubulations --$tChapter Eight Malnormality and Fiber-Products --$tChapter Nine Splicing Walls --$tChapter Ten Cutting X ? --$tChapter Eleven Hierarchies --$tChapter Twelve Virtually Special Quotient Theorem --$tChapter Thirteen Amalgams of Virtually Special Groups --$tChapter Fourteen Large Fillings Are Hyperbolic and Preservation of Quasiconvexity --$tChapter Fifteen Relatively Hyperbolic Case --$tChapter Sixteen Largeness and Omnipotence --$tChapter Seventeen Hyperbolic 3-Manifolds with a Geometrically Finite Incompressible Surface --$tChapter Eighteen Limit Groups and Abelian Hierarchies --$tChapter Nineteen Application Towards One-Relator Groups --$tChapter Twenty Problems --$tReferences --$tIndex 330 $aThis monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology. 410 0$aAnnals of Mathematics Studies 606 $aHyperbolic groups 606 $aGroup theory 610 $aCAT(0). 610 $aGromov. 610 $aThurston. 610 $ageometric group theory. 610 $agraphs of groups. 610 $ahierarchies. 610 $ahyperbolic groups. 610 $aone relator groups. 610 $arelatively hyperbolic groups. 610 $asmall cancellation theory. 610 $asubgroup separability. 610 $avirtual haken. 610 $aword hyperbolic groups. 615 0$aHyperbolic groups. 615 0$aGroup theory. 676 $a512.2 700 $aWise$b Daniel T.$f1971-$0521402 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910554261903321 996 $aThe structure of groups with a quasiconvex hierarchy$92820041 997 $aUNINA