Telescope Construction

This lecture explains the construction of a telescope visually represented by cylinders on circles, introducing the concept of colimits indexed by natural numbers. It covers examples like free products, amalgams, and push-outs in the context of group theory, illustrating how to calculate the fundamental group of a space as a colimit. The instructor demonstrates how to show that certain spaces are homotopic to circles and calculates the fundamental group of a torus knot. The lecture concludes with a detailed explanation of decomposing the complement of a knot into two open sets and calculating its fundamental group using Seifert-van Kampen's theorem.