0
$\begingroup$

Is there an example of analytic hypersurface in $C^n$ such that its fundamental group is simple i.e. does not have normal subgroups except the trivial group and the group itself ?

Thank you

EDIT : The fundamental of a hypersurface $A$ is by definition the group of its complement $\pi_1(C^n \setminus A)$.

Improve this question
$\endgroup$
12
  • 3
    $\begingroup$ The group with one element is simple (sorry for being pedantic). $\endgroup$
    – Jason Starr
    Oct 27, 2015 at 12:48
  • 1
    $\begingroup$ Are you asking whether any specified finite simple group arises as the fundamental group of some analytic hypersurface? $\endgroup$
    – Jason Starr
    Oct 27, 2015 at 12:54
  • 3
    $\begingroup$ Okaaay . . . an affine hyperplane has trivial fundamental group so that the only normal subgroups are the trivial group and the group itself. $\endgroup$
    – Jason Starr
    Oct 27, 2015 at 14:01
  • 1
    $\begingroup$ A hyperplane is isomorphic to $\mathbb{C}^{n-1}$, which is simply connected. Are you asking about the fundamental group of the complement of the hypersurface? $\endgroup$
    – Jason Starr
    Oct 27, 2015 at 15:46
  • 3
    $\begingroup$ Sorry for being pedantic :) 1: if "simple" means "has no normal subgroup", then no group is simple 2) according to all conventions, the group with 1 element is not simple (and 1 is not a prime number). $\endgroup$
    – YCor
    Oct 27, 2015 at 16:27

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.