Let \({ f: S^n \rightarrow S^n }\) be a map of degree zero. Show that there exists points \({ x, y \in S^n }\) with \({ f(x) = x }\) and \({ f(y) = – y}\). Use this to show that if F is a continuous vector field defined on the unit ball \({ D^n […]

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# Category Archives: Hatcher

## Direction of a vector field

Let \({ f: S^n \rightarrow S^n }\) be a map of degree zero. Show that there exists points \({ x, y \in S^n }\) with \({ f(x) = x }\) and \({ f(y) = – y}\). Use this to show that if F is a continuous vector field defined on the unit ball \({ D^n […]