Re: Homotopic maps

If n >= 3, let g:S^n --> S^n be the map g(x_1, ...,x_n, x_{n+1}) =
(x_1, ...., x_n, |x_{n+1}|). Notice that im g lies in the closed upper
hemisphere H of S^n which is a disk D^n. Let h: H --> S^n be the map
the takes Bd D^n to the southpole and maps int D^n onto S^n - {south
pole}. Let f(x) = h(g(x)): S^n -->> S^n. Since f factors through a disk
it's inessential. That is, f is an inessential map of S^n onto S^n.

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