(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What is the fundamental group of A where A is the 2-sphere with two disjoint disks removed. It has the same homotopy type as a familiar space.

2. Relevant equations

3. The attempt at a solution

When I first looked at this problem, and saw how it was drawn out (in Munkres book,) it looked like a squashed sphere with two holes in it, so my first thought that it was homotopic to the double tours T#T. However, since the problem states that it is not the solid 2-sphere, I'm having second thoughts about it. To me it seems like its a sphere missing two holes in one hemisphere. It doesn't say anything about performing some surgery on the space and adding a cylinder or Mobius band to it, so it seems to me that it should be homotopic to the 2-sphere and therefore it's fundamental group is trivial. Am I on the right track here?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Topology question

**Physics Forums | Science Articles, Homework Help, Discussion**