作者 Malone, William
書名 Topics in geometric group theory
國際標準書號 9781109695885
book jacket
說明 79 p
附註 Source: Dissertation Abstracts International, Volume: 71-04, 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 path-connected 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 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
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
School code: 0240
Host Item Dissertation Abstracts International 71-04B
主題 Mathematics
Theoretical Mathematics
0405
0642
Alt Author The University of Utah. Mathematics