Twisted Conjugacy classes in lattices in semisimple lie groups
Material type:
TextPublication details: 2013Description: 82pSubject(s): Online resources: Dissertation note: 2013Ph.DHBNI Abstract: Let G be a group and let Ø : Γ → Γ be an endomorphism. We define an action g.x := gxØ(g-1), for g,x ε Γ, of Γ on itself. The Ø-twisted conjugacy class of an element x ε Γ is the orbit of this action containing x. A group Γ has the R∞ -property if every automorphism Ø of Γ has infinitely many Ø-twisted conjugacy classes. In this thesis it is shown that any irreducible lattice in a non-compact connected semisimple Lie group with finite center and having real rank at least 2 has the R∞ -property. It is also shown that any countable abelian extensions Λ of Γ has the R∞-property when (i) the lattice Γ is linear, (ii) Γ is a torsion free non-elementary hyperbolic group. Also considered, the R∞-problem for S -arithmetic lattices.
THESIS & DISSERTATION
| Home library | Call number | Materials specified | URL | Status | Date due | Barcode | |
|---|---|---|---|---|---|---|---|
| IMSc Library | HBNI Th63 (Browse shelf(Opens below)) | Link to resource | Available | 69746 |
2013
Ph.D
HBNI
Let G be a group and let Ø : Γ → Γ be an endomorphism. We define an action g.x := gxØ(g-1), for g,x ε Γ, of Γ on itself. The Ø-twisted conjugacy class of an element x ε Γ is the orbit of this action containing x. A group Γ has the R∞ -property if every automorphism Ø of Γ has infinitely many Ø-twisted conjugacy classes. In this thesis it is shown that any irreducible lattice in a non-compact connected semisimple Lie group with finite center and having real rank at least 2 has the R∞ -property. It is also shown that any countable abelian extensions Λ of Γ has the R∞-property when (i) the lattice Γ is linear, (ii) Γ is a torsion free non-elementary hyperbolic group. Also considered, the R∞-problem for S -arithmetic lattices.
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