Subject: question about geometric realization From: Andre Henriques Date: Thu, 3 Feb 2005 22:26:49 -0500 (EST) To: dmd1@lehigh.edu Dear Don, Could you please distribute this question to your mailing list? Sincerely, Andre Henriques. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Let f:X. -> Y. be a map of simplicial topological spaces. Under what circumstances can one deduce that |f|:|X| -> |Y| is a Serre fibration? My guess is that it is enough for f to have the right lifting property with respect to the following three classes of maps: (1) \Lambda^{n,j}. -> \Delta^n., (2) D^m -> D^m x [0,1], and (3) (\Lambda^{n,j}. x (D^m x [0,1])) \cup (\Delta^n. x D^m) -> \Delta^n. x (D^m x [0,1]). Here, \Delta^n. is the simplicial n-simplex and D^m is the topological m-disk (viewed as a constant simplicial space). Does anyone know how to prove this? If someone has a different set of conditions to offer, that's also good. But I would like them to at least apply to the following example: Consider the 2-fold cover S1 -> S1, then apply the simplicial bar construction to get a map of simplicial spaces f:BS1. -> BS1.. Andre Henriques