Fundamental Group of Surfaces - Multiplication and Properties

Delve deeper into the fundamental group of a surface in this 35-minute lecture on Algebraic Topology. Prove that the multiplication of equivalence classes or types of loops from a base point forms a group in the algebraic sense. Explore the fundamental group of the torus and the projective plane. Learn about multiplication, identity, constant loops, inverses, and associativity through detailed proofs and picture examples. Conclude with a discussion on the projective plane and a problem to describe the fundamental group of a given space. Suitable for beginners in Algebraic Topology, this lecture is part of a course given by N J Wildberger of UNSW.