Subject: fundamental groups
Date: Tue, 7 Oct 2003 10:15:51 -0400 (EDT)
From: Haynes Miller
In connection with Mark Hovey's question
> 1. (Asked by my colleague). Is every group the fundamental group of a
> compact Hausdorff space? I know I should know the answer to this...
I note
MR0943095 (89g:55021)
Shelah, Saharon(IL-HEBR)
Can the fundamental (homotopy) group of a space be the rationals?
Proc. Amer. Math. Soc. 103 (1988), no. 2, 627--632.
>From the review:
The author proves that, for any path-connected, locally path-connected,
compact metric space, the fundamental group is either finitely generated
or of the cardinality of the continuum. In particular, the additive group
of rationals does not occur as the fundamental group of such a space.
- Haynes Miller
__________________________________________
Subject: Re: answer and questions
Date: Tue, 7 Oct 2003 14:47:49 -0400 (EDT)
From: Yuli Rudyak
This an answer:
My colleague told me: take a 2-dimensional complex with the given fundamental
group, then take its Stone-Cech compactification (but the base point must be in
the original complex, not in the crown).
Dr. Yuli B. Rudyak
Department of Mathematics
University of Florida
358 Little Hall
PO Box 118105
Gainesville, FL 32611-8105
USA
TEL: (+1) 352-392-0281 ext. 319(office)
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URL: http://www.math.ufl.edu/~rudyak/