Quasiactions on trees II : finite depth BassSerre trees
 Author/Creator
 Mosher, Lee, 1957
 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

Stacks

Unknown
QA3 .A57 NO.1008

Unknown
QA3 .A57 NO.1008
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Contributors
 Contributor
 Sageev, Michah, 1966
 Whyte, Kevin, 1970
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's Summary
 This paper addresses questions of quasiisometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the BassSerre 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 quasiisometric to the fundamental group of $\mathcal{G}$ is also the fundamental group of a finite graph of coarse Poincare duality groups, and any quasiisometry between two such groups must coarsely preserve the vertex and edge spaces of their BassSerre 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)
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Lee Mosher, Michah Sageev, Kevin Whyte.
 Title Variation
 Quasiactions on trees 2
 Quasiactions on trees two
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1008
 Note
 "November 2011, volume 214, number 1008 (fourth of 5 numbers)."
 ISBN
 9780821847121 (alk. paper)
 0821847120 (alk. paper)