Let \(f:\mathbb {R}P^3\to \mathbb {R}P^3\) be defined by \[ f([x_0:x_1:x_2:x_3])=[x_0^2:x_1^2:x_2^2:x_3^2]. \] Compute the degree and the Lefschetz number of \(f\).
Question
Math 6510 • Differentiable Manifolds
Fall 2007 • Question 2
Question
Fall 2007 • Question 2
Let \(f:\mathbb {R}P^3\to \mathbb {R}P^3\) be defined by \[ f([x_0:x_1:x_2:x_3])=[x_0^2:x_1^2:x_2^2:x_3^2]. \] Compute the degree and the Lefschetz number of \(f\).