說明 
79 p 
附註 
Source: Dissertation Abstracts International, Volume: 7104, Section: B, page: 2434 

Adviser: Mladen Bestvina 

Thesis (Ph.D.)The University of Utah, 2010 

This document contains results in a couple of nonrelated areas of geometric group theory. What follows are abstracts for each part 

Let Mi and Ni be pathconnected locally uniquely geodesic metric spaces that are not points and f : i=1mM i→i=1nNi be an isometry where i=1nN i and i=1mMi are given the sup metric. Then m = n and after reindexing Mi is isometric to Ni for all i. Moreover f is a composition of an isometry that reindexes the factor spaces and an isometry that is a product of isometries fi : Mi → Ni 

Given a geometric amalgamation of free groups G and the associated simple thick twodimensional hyperbolic piecewise manifold M, the visual boundary ∂M is a complete quasiisometry invariant. This invariant can be efficiently computed for any G using an adaptation of Leighton's Theorem 

Let G and G' be geometric amalgamation of free groups with a single Z vertex. If the associated simple thick twodimensional hyperbolic piecewise manifolds M and M' have the same Euler characteristic, then G is commensurable to G' if and only if M and M' are homeomorphic. The proof is then extended to the case where G and G' have more than a single Z vertex, but more conditions have to be placed on G and G'. With these results an elementary example of two geometric amalgamations of free groups that are quasiisometric but not commensurable can be given 

School code: 0240 
Host Item 
Dissertation Abstracts International 7104B

主題 
Mathematics


Theoretical Mathematics


0405


0642

Alt Author 
The University of Utah. Mathematics

