Let be the complement of the following subset of the plane
Prove that is a free group on a countable set of generators.
I don't know how to start this problem. Thanks in advance.
The deformation retract to the wedge product of circles would be the proper way to approach this problem.
Once you get the deformation retract, I think it would not be hard to prove this.
Last edited by aliceinwonderland; Mar 24th 2009 at 03:08 PM.
Reason: Error Correction !!