Non-uniform lattices on uniform trees / Lisa Carbone.

Format:

Book

Author/Creator:

Carbone, Lisa, 1965- author.

Series:

Memoirs of the American Mathematical Society ; no. 724.

Memoirs of the American Mathematical Society, 0065-9266 ; number 724

Language:

English

Subjects (All):

Lattice theory.

Trees (Graph theory).

Physical Description:

1 online resource (146 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2001.

Language Note:

English

Summary:

This title provides a comprehensive examination of non-uniform lattices on uniform trees. Topics include graphs of groups, tree actions and edge-indexed graphs; $Aut(x)$ and its discrete subgroups; existence of tree lattices; non-uniform coverings of indexed graphs with an arithmetic bridge; non-uniform coverings of indexed graphs with a separating edge; non-uniform coverings of indexed graphs with a ramified loop; eliminating multiple edges; existence of arithmetic bridges. This book is intended for graduate students and research mathematicians interested in group theory and generalizations.

Contents:

""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""

Notes:

"July 2001, volume 152, number 724 (end of volume)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0317-X