Ring Spectra Which Are Thom Complexes
نویسنده
چکیده
commutes up to homotopy where T is the map that exchanges factors. Let L be a space and let be a fibration over L classified by a mapf L BF (the classifying space of stable spherical fibrations). We can form the Thom spectrum T(f) of f as a suspension spectrum by letting (T(f)) be the Thorn complex of L n--YBFn where L is the n-skeleton of L. This makes T(f)-{(T(f))n) into a suspension spectrum. Spectra which arise in this fashion have a unit which is the inclusion of the fiber on the Thorn class. Natural examples of maps f:L BF give a plethora of interesting spectra: among them are K(Z2, 0), K(Z, 0), the Brown-Gitler spectrum, and a spectrum for which the secondary operation of Adams j,j [1] is defined and non-zero on the Thom class. Frequently, the Thom spectra which we obtain in this manner are commutative ring spectra. A useful feature of these Thom spectra is that they admit particularly nice resolutions. Consequently, these spectra give rise to
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