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 |uhttp://pqdd.sinica.edu.tw/twdaoapp/servlet/
advanced?query=3397582