Quasi-actions on trees II: Finite depth Bass-Serre trees

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dc.creatorMosher, Lee
dc.creatorSageev, Michah
dc.creatorWhyte, Kevin
dc.date2004-05-13
dc.date2005-09-16
dc.date.accessioned2026-07-07T05:08:12Z
dc.date.available2026-07-07T05:08:12Z
dc.descriptionThis 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 G is a finite graph of coarse Poincare duality groups then any finitely generated group quasi-isometric to the fundamental group of 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 preserves 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 G_v which is an n-dimensional coarse Poincare duality group for which every incident edge group has positive codimension: the crossing graph of G_v is a graph e_v that describes the pattern in which the codimension~1 edge groups incident to G_v are crossed by other edge groups incident to G_v, and the crossing graph condition requires that e_v be connected or empty.
dc.description104 pages in 7 sections, with table of contents, and with 3 figures. Revisions of the intro and the reference list from the previous version
dc.identifierhttps://arxiv.org/abs/math/0405237
dc.identifierhttp://arxiv.org/abs/math/0405237
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71167
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20F65
dc.titleQuasi-actions on trees II: Finite depth Bass-Serre trees
dc.typetext

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