# Quasi-actions on trees II : finite depth Bass-Serre trees

- Responsibility
- Lee Mosher, Michah Sageev, Kevin Whyte.
- Language
- English.
- Imprint
- Providence, R.I. : American Mathematical Society, 2011.
- Physical description
- v, 105 p. : ill. ; 26 cm.
- Series
- Memoirs of the American Mathematical Society ; no. 1008.

## Access

### Available online

### Math & Statistics Library

**Stacks**

Call number | Status |
---|---|

QA3 .A57 NO.1008 | Unknown |

### More options

## Creators/Contributors

- Author/Creator
- Mosher, Lee, 1957-
- Contributor
- Sageev, Michah, 1966-
- Whyte, Kevin, 1970-

## Contents/Summary

- Bibliography
- Includes bibliographical references and index.
- Publisher's Summary
- This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poincare duality groups. The main theorem says that, under certain hypotheses, if $\mathcal{G}$ is a finite graph of coarse Poincare duality groups, then any finitely generated group quasi-isometric to the fundamental group of $\mathcal{G}$ is also the fundamental group of a finite graph of coarse Poincare duality groups, and any quasi-isometry between two such groups must coarsely preserve the vertex and edge spaces of their Bass-Serre trees of spaces. Besides some simple normalization hypotheses, the main hypothesis is the "crossing graph condition", which is imposed on each vertex group $\mathcal{G}_v$ which is an $n$-dimensional coarse Poincare duality group for which every incident edge group has positive codimension: the crossing graph of $\mathcal{G}_v$ is a graph $\epsilon_v$ that describes the pattern in which the codimension 1 edge groups incident to $\mathcal{G}_v$ are crossed by other edge groups incident to $\mathcal{G}_v$, and the crossing graph condition requires that $\epsilon_v$ be connected or empty.

(source: Nielsen Book Data)9780821847121 20160606

## Subjects

## Bibliographic information

- Publication date
- 2011
- Title Variation
- Quasi-actions on trees 2
- Quasi-actions on trees two
- Series
- Memoirs of the American Mathematical Society, 0065-9266 ; no. 1008
- Note
- "November 2011, volume 214, number 1008 (fourth of 5 numbers)."
- ISBN
- 9780821847121 (alk. paper)
- 0821847120 (alk. paper)