Subject: questions on homotopy of simplicial spaces
Date: Fri, 11 Apr 2003 11:33:51 -0400 (EDT)
From: Ping Xu <ping@math.psu.edu>

I have some questions regarding simplicial spaces.

Many thanks

Ping

.........

(1) If $X$ is a CW complex, it is standard that
any element in $H^2 (X, Q)$ induces a map  from $X$ to $K(Q, 2)$.
The question is whether it is still true  if $X$ is
replaced by a simplicial CW complex $X.=X_n, n \in N $.
Here $K(Q, 2)$ is considered as a simplicial space with face and
degeneracy maps equal to the identity, and
a map means  "a simplicial map".
If so, what is a good reference?

(2) Let $M=M_n, n \in N $ be a simplicial manifold.
Does the set of simplicial G bundles over M. one-one
correspond  to  the set of G bundles over the simplicial realization ||M.||
 of M? If it is not true in general, what about if each $M_n$ is
compact? What is a reference?