Algebraic Topology · Problem 2C.2

Cohomology — Allen Hatcher

Mathematics — Topology · lefschetz-fixed-point-sphere

Problem

Use the Lefschetz fixed point theorem to show that a map Sn→SnS^n \to S^n has a fixed point unless its degree is equal to the degree of the antipodal map x↦−xx \mapsto -x.

Related theory

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