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) TEL: (+1) 352-381-8497(home) FAX: (+1) 352-392-8357 URL: http://www.math.ufl.edu/~rudyak/