Rips construction and Kazhdan property (T).

DOI10.4171/GGD/29zbMath1152.20039arXivmath/0605553MaRDI QIDQ2475042

Igor Belegradek, Denis V. Osin

Publication date: 20 March 2008

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605553

zbMATH Keywords

finitely generated groupsfinitely presented groupsrelatively hyperbolic groupssmall cancellation conditionsKazhdan property (T)Rips construction

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Automorphism groups of groups (20F28) Hyperbolic groups and nonpositively curved groups (20F67) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items (16)

The bi-embeddability relation for finitely generated groups. II ⋮ The Bass-Jiang group for automorphism-induced HNN-extensions ⋮ Rips construction without unique product ⋮ Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients ⋮ The triviality problem for profinite completions ⋮ Some applications of group-theoretic Rips constructions to the classification of von Neumann algebras ⋮ Post's correspondence problem: from computer science to algebra ⋮ Post's Correspondence Problem for hyperbolic and virtually nilpotent groups ⋮ Detecting ends of residually finite groups in profinite completions ⋮ Small cancellations over relatively hyperbolic groups and embedding theorems. ⋮ Non-aspherical ends and non-positive curvature ⋮ A non-residually finite group acting uniformly properly on a hyperbolic space ⋮ New nonlinear hyperbolic groups ⋮ Examples of groups whose automorphisms have exotic growth ⋮ Infinitely presented small cancellation groups have the Haagerup property ⋮ New examples of \({W}^\ast\) and \({C}^\ast \)-superrigid groups

Cites Work

• Nonarithmetic superrigid groups: Counterexamples to Platonov's conjecture
• The proalgebraic completion of rigid groups.
• The SQ-universality and residual properties of relatively hyperbolic groups.
• ENDOMORPHISMS OF RELATIVELY HYPERBOLIC GROUPS
• Unsolvable Problems About Small Cancellation and Word Hyperbolic Groups

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