Re: [math-fun] Klein bottle puzzles

25 Nov 2020

      Andy Latto wrote:

   𝜒(M) = 2 - 2 g

[for orientable surfaces M].

Yes, sorry about that.

And as he almost wrote:

   𝜒(M) = 2 - g

for nonorientable compact surfaces.

Examples: 

   𝜒(S^2)  =  2

   𝜒(Klein bottle)  =  2 - 2  =  0.

   𝜒(3-holed torus)  =  2 - 2*3  =  -4.

   𝜒(P # P # P)  =  2 - 3  =  -1.

—Dan

Dan Asimov