Lecture 9
Ch. 2, end of sec 3, and sec. 4.
Explain the dependence of the fundemental group on the basepoint.
Describe the effect of a continuous mapping on the fundamental group.
Show that it is a group homomorphism. Define the notion of homotopic maps,
and relative homotopy. Explain theorem 4.1. Do not discuss the notion of a
retract or deformation retract (I'm saving this for Lecture 12).
Ideas: Explain these important notions intuitively, draw schematic pictures to
accompany your abstract definitions. Discuss exercise 4.1. Give examples
of homotopic maps, relatively homotopic maps, and homotopic maps which are
NOT relatively homotopic.