18.904: Lecture 1

Lecture 1

Massey: Ch. 1, Sec. 2-3.

Define the notion of an n-manifold, and give examples. Discuss orientability.

Some ideas: how exactly is S^n seen to satisfy the definition of an n-manifold? You could give other examples - consulting other references perhaps - but Lecure 2 is devoted to talking about the examples which are compact surfaces, so try to not dwell on these. Non-examples could be discussed. Is the closed unit disk an manifold? Why or why not? What does orientability mean intuitively? Rigorously? How does the determinant condition fit into the Mobius band example? Is S^n orientable for all n?