Further Applications to Spheres

(16.1) Proposition. Let r:Sⁿ → Sⁿ be the reflection r(x ₀, …, x_n ) = (–x ₀, x ₁, …, x_n ). Then the induced homomorphism H n ( r ) : H n ( S n ) → H n ( S n ) https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429502408/daca2c81-d126-4847-864b-0573337f4417/content/eq398.tif"/>