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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2005 • Question 10

Question

Math 6510 • Differentiable Manifolds Winter 2005 • Question 10

Let \(X\) and \(Y\) be two closed oriented manifolds. Prove that Euler characteristic is multiplicative, i.e. that \[ \chi (X\times Y)=\chi (X)\times \chi (Y). \] You may not appeal to the Kunneth formula.

Raw LaTeX

Let \(X\) and \(Y\) be two closed oriented manifolds. Prove that Euler characteristic
is multiplicative, i.e. that
\[
  \chi(X\times Y)=\chi(X)\times\chi(Y).
\]
You may not appeal to the Kunneth formula.

Topic Tags

Differential Forms and Exterior Calculus Euler Characteristic and Lefschetz Fixed Point Theorem Homotopy and Degree on Manifolds Orientability and Volume Forms