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I am just an Algebraic Topology beginner and I have one doubt related to the relationship between the topological space and the fundamental group. As we know that if given a specific topological space, we can calculate the fundamental group of it. Therefore, my question is that if given a fundamental group, can we define a particular topological space for it? How?

I hope you do not mind me and provide me with some intuitions on this problem.

Thanks!

David James
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    Yes, this an extremely well-studied question. You can find it an Appendix of the book by Hatcher or a more general construction here. – ThePuix Jul 14 '19 at 15:36
  • @ThePuix Thanks for helping me ! – David James Jul 14 '19 at 15:51
  • He asked me this question since I recently finished the fundamental group calculation and started to do on covering spaces. He also specified that we can define a particular topological space for it, but I still do not know how. – David James Jul 14 '19 at 15:59

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