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