Subject: Question for discussion group
Date: Thu, 10 Jan 2002 15:52:28 +0100 (MET)
From: Rasmus Ejlers Moegelberg
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