Subject: Re: quasifibration query Date: Tue, 15 May 2001 14:31:28 -0500 From: Charles Rezk To: Don Davis CC: rezk@math.nwu.edu Tom Goodwille wrote: > >Def: A map p:E->B of spaces is a quasifibration (QF) if for every > >point in B the canonical map from the fiber of p to the homotopy > >fiber of p is a weak homotopy equivalence. > As I half-suspected, I was wrong about this. This is a consequence of my > > unfortunate habit of learning things by hearsay or osmosis rather than > studying things thoroughly! For years I have had the erroneous idea > (which I have even stated in print) that "quasifibration" means what > I said above. In fact "quasifibration" is a stronger condition; it's > probably the same one that I (re)discovered for myself > and called "UQF" in my query. I should go to the library. Dold & Thom, "Quasifaserungen und Symmetrische Produkte", Annals 1958, give a definition of quasifibrations (Definition 1.1) which is almost identical to the definition (QF) Tom gave. They go on to give an example (Bemerkung 2.3) which shows that QF does not imply UQF. I presume that this is the paper in which quasifibrations were first introduced. If "quasifibration" now really means UQF, then it's definition must have changed somewhere along the line. I would also be curious to see a reference to the UQF property in the literature, in particular the characterization in terms of pullbacks along maps from disks. -- Charles