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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2006 • Question 4

Question

Math 6510 • Differentiable Manifolds Winter 2006 • Question 4

  1. State the Lefschetz fixed point theorem (for Lefschetz maps).
  2. Compute the Lefschetz number of the identity map \(id:\mathbb {C}P^2\to \mathbb {C}P^2\) by first perturbing it to a Lefschetz map and then applying the Lefschetz fixed point theorem.

Raw LaTeX

\begin{enumerate}
\item State the Lefschetz fixed point theorem (for Lefschetz maps).
\item Compute the Lefschetz number of the identity map
\(id:\mathbb{C}P^2\to\mathbb{C}P^2\) by first perturbing it to a Lefschetz map and then
applying the Lefschetz fixed point theorem.
\end{enumerate}

Topic Tags

Euler Characteristic and Lefschetz Fixed Point Theorem Fixed Point Theorems and Borsuk-Ulam