2
$\begingroup$

Determine the Euler characteristic of the surface

$ M=\left\{(x,y,z); \sqrt{x^2+y^2}=1+z^{2n}, 0< z< 1\right\} $

  • 5
    This doesn't look compact to me...2010-08-26

1 Answers 1

3

For any $n\in \mathbb{R}$, your surface is a cylinder, and homotopic to the circle.

(I don't see why Agusti Roig gets the disjoint union of two cylinders)