Subject: Question for discussion group
Date: Thu, 10 Jan 2002 15:52:28 +0100 (MET)
From: Rasmus Ejlers Moegelberg <mogel@math.ku.dk>
To: dmd1@lehigh.edu

Hi there,

I have a question for the discussion group. A theorem of Milnor says that
if A and B are CW-complexes and h:A->B is any map between them, then the
homotopy fiber of h is homotopy equivalent to a CW-complex. Is it true,
that if A and B are only homotopy equivalent to CW-complexes, then the
homotopy fiber of h is homotopy equivalent to a CW-complex?

I have a different question, that would answer the above question for me:
Suppose we have a (strictly) commutative diagram of maps:

A ----h----> B
|            |
v            v
A' ---h'---> B'

where the two vertical maps are homotopy equivalences. Is the induced map
from the homotopy fiber of h to the homotopy fiber of h' a homotopy
equivalence, and not just a weak homotopy equivalence?

Rasmus Ejlers Mogelberg,
Student, University of Copenhagen, Denmark