Paper 1, Section II, G

Algebraic Topology
Part II, 2009

Let XX be the space obtained by identifying two copies of the Möbius strip along their boundary. Use the Seifert-Van Kampen theorem to find a presentation of the fundamental group π1(X)\pi_{1}(X). Show that π1(X)\pi_{1}(X) is an infinite non-abelian group.