What is the range of the fundamental group?

Asked Jun 22 '11 at 10:08

Active Jun 22 '11 at 10:29

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is the group of rational numbers the fundamental group of some space?

Given any group G,can we find a complex X whose fundamental group is G.If not,which kind of group satisfies this condition?

edited Apr 13 '17 at 12:20

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asked Jun 22 '11 at 10:08

Strongart

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Yes, such space exists for any group. See e.g. http://en.wikipedia.org/wiki/Classifying_space – Grigory M Jun 22 '11 at 10:12

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