|
|
|||
|
||||
OverviewThis 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. Full Product DetailsAuthor: Lee Mosher , Michah Sageev , Kevin WhytePublisher: American Mathematical Society Imprint: American Mathematical Society Edition: New ed. Volume: 1008 Weight: 0.192kg ISBN: 9780821847121ISBN 10: 0821847120 Pages: 105 Publication Date: 30 October 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: To order Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |