Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science

2013-02-26

2013

Λέντζος Κωνσταντίνος

Δημήτριος Βάρσος Καθηγ. (Επιβλέπων),Ιωάννης Εμμανουήλ Καθηγ. ,Μιχαήλ Συκιώτης Επικ. Καθηγ.

Αυτομορφισμοί ελεύθερων ομάδων και train tracks

Greek

Automorphisms of free groups and train tracks

In our work we study the group of automorphisms of free groups. In the first
two sections we present free groups and their fundamental properties. We next
define the concept of the group presentation and analyze Dehn's problems. The
proofs that free groups are residually finite and Hopfian, are also provided.
In the third section we develop Nielsen's method for studying the automorphisms
of free groups. Then we prove that the equalizer of two monomorphisms of
finitely generated free groups is finitely generated following the
corresponding work of J.Stallings. In the following sections we set the
background for Bestvina-Handel's theorem on outer automorphisms of free groups
and present an algorithm for finding an irreducible topological representative
with very interesting properties, the so-called train track.

Free groups, Nielsen method, Outer automorphisms, Train tracks

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https://pergamos.lib.uoa.gr/uoa/dl/object/1316452