Author | Bass, Hyman. author |
---|---|
Title | Tree Lattices [electronic resource] / by Hyman Bass, Alexander Lubotzky |
Imprint | Boston, MA : Birkhรคuser Boston, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2098-5 |
Descript | XIII, 233 p. online resource |
0 Introduction -- 0.1 Tree lattices -- 0.2 X-lattices and H-lattices -- 0.3 Near simplicity -- 0.4 The structure of tree lattices -- 0.5 Existence of lattices -- 0.6 The structure of A = ?\X -- 0.7 Volumes -- 0.8 Centralizers, normalizers, commensurators -- 1 Lattices and Volumes -- 1.1 Haar measure -- 1.2 Lattices and unimodularity -- 1.3 Compact open subgroups -- 1.5 Discrete group covolumes -- 2 Graphs of Groups and Edge-Indexed Graphs -- 2.1 Graphs -- 2.2 Morphisms and actions -- 2.3 Graphs of groups -- 2.4 Quotient graphs of groups -- 2.5 Edge-indexed graphs and their groupings -- 2.6 Unimodularity, volumes, bounded denominators -- 3 Tree Lattices -- 3.1 Topology on G = AutX -- 3.2 Tree lattices -- 3.3 The group GH of deck transformations -- 3.5 Discreteness Criterion; Rigidity of (A, i) -- 3.6 Unimodularity and volume -- 3.8 Existence of tree lattices -- 3.12 The structure of tree lattices -- 3.14 Non-arithmetic uniform commensurators -- 4 Arbitrary Real Volumes, Cusps, and Homology -- 4.0 Introduction -- 4.1 Grafting -- 4.2 Volumes -- 4.8 Cusps -- 4.9 Geometric parabolic ends -- 4.10 ?-parabolic ends and ?-cusps -- 4.11 Unidirectional examples -- 4.12 A planar example -- 5 Length Functions, Minimality -- 5.1 Hyperbolic length (cf. [B3], II, ยง6) -- 5.4 Minimality -- 5.14 Abelian actions -- 5.15 Non-abelian actions -- 5.16 Abelian discrete actions -- 6 Centralizers, Normalizers, and Commensurators -- 6.0 Introduction -- 6.1 Notation -- 6.6 Non-minimal centralizers -- 6.9 N/?, for minimal non-abelian actions -- 6.10 Some normal subgroups -- 6.11 The Tits Independence Condition -- 6.13 Remarks -- 6.16 Automorphism groups of rooted trees -- 6.17 Automorphism groups of ended trees -- 6.21 Remarks -- 7 Existence of Tree Lattices -- 7.1 Introduction -- 7.2 Open fanning -- 7.5 Multiple open fanning -- 8 Non-Uniform Lattices on Uniform Trees -- 8.1 Carboneโs Theorem -- 8.6 Proof of Theorem (8.2) -- 8.7 Remarks -- 8.8 Examples. Loops and cages -- 8.9 Two vertex graphs -- 9 Parabolic Actions, Lattices, and Trees -- 9.0 Introduction -- 9.1 Ends(X) -- 9.2 Horospheres and horoballs -- 9.3 End stabilizers -- 9.4 Parabolic actions -- 9.5 Parabolic trees -- 9.6 Parabolic lattices -- 9.8 Restriction to horoballs -- 9.9 Parabolic lattices with linear quotient -- 9.10 Parabolic ray lattices -- 9.13 Parabolic lattices with all horospheres infinite -- 9.14 A bounded degree example -- 9.15 Tree lattices that are simple groups must be parabolic -- 9.16 Lattices on a product of two trees -- 10 Lattices of Nagao Type -- 10.1 Nagao rays -- 10.2 Nagaoโs Theorem: r = PGL2(Fq[t]) -- 10.3 A divisible (q + l)-regular grouping -- 10.4 The PNeumann groupings -- 10.5 The symmetric groupings -- 10.6 Product groupings