Re: fundamental group of R^3 - n lines through the origin

From: Travis Willse (twillse_at_gladstone.uoregon.edu)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 01:59:57 -0800

s,

Consider the function standard mapping from R^3\{0} to RP^2:

f(x,y,z)=[x,y,z]/sqrt(x^2+y^2+z^2). Removing a line through the origin
is the same as removing a point in RP^2. What can you say about the
fundamental group of R^3\{n lines}?

(The above argument doesn't apply to the trivial n=0 case, in which case
0 remains in the space, and f isn't well-defined.)

Travis

s wrote:
> Does anyone know how to compute the fundamental group of R^3 \ n lines
> through the origin. Even the case n=2 seems non trivial - at least to
> give a decent proof.
>