Quasi-Isometry invariants and Cut-Sets

Doctoral Dissertation uoadl:1308810 346 Read counter

Unit:
Τομέας Άλγεβρας Γεωμετρίας
Library of the School of Science
Deposit date:
2015-03-31
Year:
2015
Author:
Γιαννουδοβαρδή Μάρθα - Καλλιόπη
Dissertation committee:
Παναγιώτης Παπάζογλου Καθηγητής (επιβλέπων), Δημήτριος Βάρσος Καθηγητής,Ολυμπία Ταλέλλη Καθηγήτρια
Original Title:
Διασπάσεις Ομάδων και Σχεδόν Ισομετρίες
Languages:
Greek
Translated title:
Quasi-Isometry invariants and Cut-Sets
Summary:
This thesis is divided in two parts; in the first part we study vertex
transitive graphs in relation to group theory, and in the second part we
study some quasi-isometry invariants of geometric group theory.
Specifically, we start by examining isoperimetric inequalities and we
prove rough structure theorems for vertex transitive graphs, furthering
the work of DeVos and Mohar. In the second part, on a joint work with
Funar and Otera, we study the growth of semistability and the simple
connectivity at infinity of hyperbolic groups. We prove that the
semistability growth of a hyperbolic group is linear, and when the group
is simply connected to infinity then the growth of the simple connectivity
at infinity is also linear.
Keywords:
Quasi-isometries, Semistability, Hyperbolic, Simple connectivity at infinity, Symmetric graphs
Index:
Yes
Number of index pages:
2
Contains images:
Yes
Number of references:
35
Number of pages:
III, 76
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