Euler characteristic of a compact surface

Question

Determine the Euler characteristic of the surface

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

For $n \in \mathbb{N}$ (including n=0), you just have one cylinder. For non-positive integers, the disjoint union of two cylinders. — Agustí Roig, Aug 26 '10 at 13:00

score 4 · Answer 1 · answered May 13 '11 at 21:38

4

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)

answered May 13 '11 at 21:38

Eric Naslund

1 Answers1