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Item Details
| Title:
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QUASI-ACTIONS ON TREES II
FINITE DEPTH BASS-SERRE TREES |
| By: |
Lee Mosher, Michah Sageev, Kevin Whyte |
| Format: |
Paperback |
| List price:
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£73.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821847120 |
| ISBN 13: |
9780821847121 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 October, 2011 |
| Edition: |
New ed. |
| Series: |
Memoirs of the American Mathematical Society 1008 |
| Pages: |
105 |
| Description: |
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. |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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