Subject: nonorietable bundles From: "John Olsen" Date: Thu, 25 Jan 2007 13:01:50 -0300 What can be said about the cohomology H^*(DE, SE; Q) (or integer coefficients) if the vector bundle E over B is nonorientable? Are the dim in which they occur the same as if the bundle was orientable? Are the dimensions then bounded above by those as if the bundle is orientable? I am thinking of applications to the Morse theory of a Morse Bott function on the free loop space. Best, John Olsen John Olsen http://www.johno.dk