Constructing product fibrations by means of
a generalization of a theorem of Ganea
Abstract: A theorem of Ganea shows that for the principal homotopy fibration induced from a fibration , there is a product decomposition . We will determine the conditions for a fibration to yield a product decomposition and generalize it to pushouts. Using this approach we recover some decompositions originally proved by very computational methods. The results are then applied to produce, after localization at an odd prime , homotopy decompositions for for some which include the cases . The factors of consist of the homotopy fibre of the attaching map for and combinations of spaces occurring in the Snaith stable decomposition of .
Affiliation: Department of Mathematics, University of Toronto, 100 St. George St., Toronto, Ontario, Canada M5S 1A1
Received by editor(s): August 9, 1994
Additional Notes: Research partially supported by a grant from NSERC
Article copyright: © Copyright 1996 American Mathematical Society