6
$\begingroup$

Let $N^2_g$ be a non-orientable closed genus $g\geq 2$ surface. Is there a way to explicitly list the normal subgroups of $\pi_1(N^2_g)$ in terms of generators and relations? I am interested in understanding all possible normal coverings of $N^2_g$.

Thank you.

$\endgroup$
  • 1
    $\begingroup$ I assume that you are familiar with the fundamental group of non-orientable closed genus $g\ge 2$ surfaces $N_g^2$, namely $\pi_1(N_g^2,\ast)=\langle x_1,...,x_g|x_1^2\cdots x_g^2\rangle$. This paper tells you something about subgroups (not necessarily normal) of orientable genus $g$ surfaces. Maybe it is helpful to get a feeling for the general procedure. $\endgroup$ – Daniel Bernoulli Oct 5 '15 at 13:01
  • 1
    $\begingroup$ The cardinality of the set of normal subgroups is continuum, hence, listing (in any meaningful sense) such subgroups is impossible. $\endgroup$ – Moishe Kohan Jan 3 at 13:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.