Subject: simplicial spaces From: Rainer Vogt Date: Mon, 12 Mar 2007 16:46:09 +0100 I have two questions about realizations of simplicial spaces for the topology community. Here simplicial space means a simplicial object in TOP and not a bisimplicial set. It is well known that the realization functor preserves pullbacks of simplicial spaces and that the fat realization (degeneracies are disregarded) preserves products up to homotopy. Does the fat realization also preserve pullbacks up to homotopy? Recall that the diagonal preserves homotopy pullbacks of bisimplicial sets provided the \pi_* condition holds (Bousfield-Friedlander-Thm.) Is there an analogue for simplicial spaces such as that the topological realization of certain homotopy pullbacks is a homotopy pullback? The statement is true for fiber sequences F_n --> E_n --> B_n provided each B_n is path connected and numerably contractible. Is there anything known for more general B_n? Best regards Rainer Prof. Dr. Rainer Vogt Studiendekan Direktor des Instituts fuer Mathematik Fachbereich Mathematik/Informatik Prof. Dr. Rainer Vogt Studiendekan Direktor des Instituts fuer Mathematik Fachbereich Mathematik/Informatik Albrechtstrasse 28 Osnabrueck 49076 Germany