8
$\begingroup$

A problem asks me to find all the covering spaces of a Klein bottle. This needs to calculate all the subgroups of the fundamental group of the Klein bottle. But I don't have any idea how to do it.

I googled it and an article says

The subgroups of the fundamental group of the Klein bottle are either trivial, free of rank one, free Abelian of rank two, or non-Abelian of rank two.

I don't know how to get the result and what is the concrete form of the subgroups (which is needed to calculate the covering spaces.)

Can you please help? Thank you.

  • 0
    Once you know the group type (up to isomorphism), computing the inclusion map is easy enough, so "computing" the covering map is a relatively standard step from there.2011-04-22

0 Answers 0