Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Spanos Panagiotis
Supervisors info:
Βάρσος Δημήτριος, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Ράπτης Ευάγγελος, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Συκιώτης Μιχαήλ, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Εξωτερικοί Αυτομορφισμοί Ομάδων Επιφανειών
Translated title:
Outer Automorphisms of Surface Groups
Summary:
Let a surface of positive genus. The extended mapping class group is defined as the quotient group of homeomorphisms from the surface to itself modulo homeomorphisms homotopic to the identity. In this master's thesis we present a proof of the Dehn, Nielsen, Baer theorem which states that the extended mapping class group is isomorphic to the group of outer automorphisms of the fundamental group of the surface. The basic tools used in the proof come from the hyperbolic structure of the surface, when the genus is greater or equal to 2.
Main subject category:
Science
Keywords:
group theory, geometric group theory, hyperbolic geometry, algebraic topology, mapping class group, modular group, outer automorphism, isotopy, surface groups, fundamental group, Dehn, Nielsen, Baer, hyperbolic surfaces
