Non-Uniform Lattices on Uniform Trees.
Carbone, Lisa.
Non-Uniform Lattices on Uniform Trees. - 1st ed. - 1 online resource (146 pages) - Memoirs of the American Mathematical Society ; v.152 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- 0. Introduction -- 1. Graphs of groups, tree actions and edge-indexed graphs -- 1.1 Graphs of groups -- 1.2 Group actions on trees and quotient graphs of groups -- 1.3 Edge-indexed graphs and their groupings -- 1.4 Existence of finite groupings -- 2. Aut(X) and its discrete subgroups -- 2.1 Tree lattices -- 2.2 The group G[sub(H)] of deck transformations -- 2.3 Constructing tree lattices -- 3. Existence of tree lattices -- 3.1 Locally compact groups and their lattices -- 3.2 Lattice Existence Theorem -- 3.3 Existence of non-uniform lattices on uniform trees -- 3.4 Existence of non-uniform coverings -- 4. Non-uniform coverings of indexed graphs with an arithmetic bridge -- 4.1 Geometric and arithmetic bridges in indexed graphs -- 4.2 Changing the ramification factor of an arithmetic bridge -- 4.3 Gluing unimodular subgraphs along connected intersections -- 4.4 Open fanning of arithmetic bridges -- 4.5 Indexed topological coverings -- 4.6 Step 1 - Schematic diagram -- 4.7 Step 2 - Construct topological covering -- 4.8 Step 3 - Change the ramification factor -- 4.9 Step 4 - Construct rectangles -- 4.10 Step 5 - Glue rectangles iteratively -- 4.11 Step 6 - Adjoin bridges -- 4.12 Step 7 - Multiple open fanning -- 4.13 Edge with a common factor implies non-uniform covering -- 5. Non-uniform coverings of indexed graphs with a separating edge -- 6. Non-uniform coverings of indexed graphs with a ramified loop -- 7. Eliminating multiple edges -- 7.1 Simplification of a graph with no loops -- 7.2 Graphs with multiplicities -- 7.3 Reduced factorization of an indexed graph -- 7.4 Canonical simplification of a unimodular indexed graph with no loops -- 8. Existence of arithmetic bridges -- 8.1 Unramified Loops -- 8.2 Completion -- 8.3 Suspension -- 8.4 Restriction -- Bibliography.
9781470403171
Lattice theory.
Trees (Graph theory).
Electronic books.
QA171.5 -- .C37 2001eb
510 s;511.3/3
Non-Uniform Lattices on Uniform Trees. - 1st ed. - 1 online resource (146 pages) - Memoirs of the American Mathematical Society ; v.152 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- 0. Introduction -- 1. Graphs of groups, tree actions and edge-indexed graphs -- 1.1 Graphs of groups -- 1.2 Group actions on trees and quotient graphs of groups -- 1.3 Edge-indexed graphs and their groupings -- 1.4 Existence of finite groupings -- 2. Aut(X) and its discrete subgroups -- 2.1 Tree lattices -- 2.2 The group G[sub(H)] of deck transformations -- 2.3 Constructing tree lattices -- 3. Existence of tree lattices -- 3.1 Locally compact groups and their lattices -- 3.2 Lattice Existence Theorem -- 3.3 Existence of non-uniform lattices on uniform trees -- 3.4 Existence of non-uniform coverings -- 4. Non-uniform coverings of indexed graphs with an arithmetic bridge -- 4.1 Geometric and arithmetic bridges in indexed graphs -- 4.2 Changing the ramification factor of an arithmetic bridge -- 4.3 Gluing unimodular subgraphs along connected intersections -- 4.4 Open fanning of arithmetic bridges -- 4.5 Indexed topological coverings -- 4.6 Step 1 - Schematic diagram -- 4.7 Step 2 - Construct topological covering -- 4.8 Step 3 - Change the ramification factor -- 4.9 Step 4 - Construct rectangles -- 4.10 Step 5 - Glue rectangles iteratively -- 4.11 Step 6 - Adjoin bridges -- 4.12 Step 7 - Multiple open fanning -- 4.13 Edge with a common factor implies non-uniform covering -- 5. Non-uniform coverings of indexed graphs with a separating edge -- 6. Non-uniform coverings of indexed graphs with a ramified loop -- 7. Eliminating multiple edges -- 7.1 Simplification of a graph with no loops -- 7.2 Graphs with multiplicities -- 7.3 Reduced factorization of an indexed graph -- 7.4 Canonical simplification of a unimodular indexed graph with no loops -- 8. Existence of arithmetic bridges -- 8.1 Unramified Loops -- 8.2 Completion -- 8.3 Suspension -- 8.4 Restriction -- Bibliography.
9781470403171
Lattice theory.
Trees (Graph theory).
Electronic books.
QA171.5 -- .C37 2001eb
510 s;511.3/3