Betti Numbers and De Rham’s Theorem
When can we be certain that a closed form will be exact?
THE lack of simple connectivity is but one measure of topological complexity for a space. In this chapter we shall deal with others, the Betti numbers, and their relations with the potentials for closed exterior forms initiated in Chapter 5. This subject is a part of the discipline called algebraic topology.
13.1. Singular Chains and Their Boundaries
What does Stokes’s theorem say for a Möbius band?
13.1a. Singular Chains
The standard (euclidean) p-simplex in p is the convex set Δp ⊂ p generated by the p + 1 points
We shall ...