MARC 主機 00000nam  2200409   4500 
001    AAI3397582 
005    20101111135944.5 
008    101111s2010    ||||||||||||||||| ||eng d 
020    9781109695885 
035    (UMI)AAI3397582 
040    UMI|cUMI 
100 1  Malone, William 
245 10 Topics in geometric group theory 
300    79 p 
500    Source: Dissertation Abstracts International, Volume: 71-
       04, Section: B, page: 2434 
500    Adviser: Mladen Bestvina 
502    Thesis (Ph.D.)--The University of Utah, 2010 
520    This document contains results in a couple of nonrelated 
       areas of geometric group theory. What follows are 
       abstracts for each part 
520    Let Mi and Ni be path-connected locally uniquely geodesic 
       metric spaces that are not points and f :   i=1mM i&
       rarr;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 
520    Given a geometric amalgamation of free groups G and the 
       associated simple thick two-dimensional hyperbolic 
       piecewise manifold  M, the visual boundary ∂M is a 
       complete quasi-isometry invariant. This invariant can be 
       efficiently computed for any G using an adaptation of 
       Leighton's Theorem 
520    Let G and G' be geometric amalgamation of free groups with
       a single Z vertex. If the associated simple thick two-
       dimensional 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 quasi-
       isometric but not commensurable can be given 
590    School code: 0240 
650  4 Mathematics 
650  4 Theoretical Mathematics 
690    0405 
690    0642 
710 2  The University of Utah.|bMathematics 
773 0  |tDissertation Abstracts International|g71-04B 
856 40 |u