The Fundamental Group and Some of Its Applications, III

Aslı Güçlükan İlhan, Dokuz Eylül University.
Date: 7th and 14th of March, 2018, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this series of talks, we will introduce the fundamental group
and discuss some of its applications including the proof of the
fundamental theorem of algebra. In this talk, we will prove that every
group can be realized as a fundamental group. We will also discuss
the theory of covering spaces for graphs. As a consequence, we show that
every subgroup of a free group is free. If time permutes, we give a quick
introduction to basic notions of homotopy theory such as cofibrations,
fibrations and weak equivalences.