Quasi Actions on Trees II Finite Depth Bass Serre Trees is popular PDF and ePub book, written by Lee Mosher in 2011, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Quasi Actions on Trees II Finite Depth Bass Serre Trees can be Read Online from any device for your convenience.
Quasi Actions on Trees II Finite Depth Bass Serre Trees Book PDF 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.
Detail Book of Quasi Actions on Trees II Finite Depth Bass Serre Trees PDF
- Author : Lee Mosher
- Release : 29 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821847121
- Genre : Mathematics
- Total Page : 118 pages
- Language : English
- PDF File Size : 18,8 Mb
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