Subject: Re: two postings From: Martin Cadek Date: Fri, 26 Jan 2007 08:40:49 +0100 On Thu, Jan 25, 2007 at 11:39:20AM -0500, Don Davis wrote: >> 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? In this case there is also a Thom class in cohomology with local coefficients and Thom isomorphism but between cohomology groups with different local coefficients. For a precise statement see the first proposition in my paper The cohomology of BO(n) with twisted integer coefficients, J. Math. Kyoto Univ. 39(1999), 277-286, or Spanier's book, exercise F in Chapter I and J in Chapter V. With best wishes, Martin Cadek