# Homotopy 同伦 & Fundamental Groups

NJ Wildberger AlgTop24: The fundamental group

Homotopy 同伦: When playing skip rope, the 2 ends of the rope are held by 2 persons while a 3rd person jumping over the “swings of rope” – these swings at any instant are  homotopic.

Fundamental Group of Surface $\pi (M; \alpha)$

Fundamental Group of Torus $\pi (T) = Z.Z$

Fundamental Group of Projective Plane (Torsion ) $\pi (P) =Z_{2}$