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Hatcher-Algebraic-Topology
· Problem 2C.2
Cohomology
Mathematics — Graph Theory · lefschetz-fixed-point-sphere
Problem
Use the Lefschetz fixed point theorem to show that a map
S
n
→
S
n
S^n \to S^n
S
n
→
S
n
has a fixed point unless its degree is equal to the degree of the antipodal map
x
↦
−
x
x \mapsto -x
x
↦
−
x
.
Related theory
Wilson Fisher Fixed Point
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