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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2004 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2004 • Question 3

Compute the Lefschetz number of the mapping \[ f_k:\mathbb {C}P^n\to \mathbb {C}P^n \] given by \[ [x_0:x_1:\cdots :x_n]\mapsto [x_0^k:x_1^k:\cdots :x_n^k] \] for \(k=1,2,\cdots \).

Raw LaTeX

Compute the Lefschetz number of the mapping
\[
  f_k:\mathbb{C}P^n\to\mathbb{C}P^n
\]
given by
\[
  [x_0:x_1:\cdots:x_n]\mapsto[x_0^k:x_1^k:\cdots:x_n^k]
\]
for \(k=1,2,\cdots\).

Topic Tags

Euler Characteristic and Lefschetz Fixed Point Theorem