Abstract
Recall that a String manifold is a Spin manifold M together with a trivialization of the class usually denoted p1(M)/2; this is a characteristic class, defined only for Spin manifolds, so that twice it is the usual first Pontrjagin class. The bordism spectrum of String manifolds is called MString or MO〈8〉; it is the Thom spectrum of the map BO〈8〉 −→ BO of the 7-connected cover of BO to BO. Similarly, MU〈6〉 is the bordism spectrum associated with the 5-connected cover BU〈6〉 −→ BU of BU .
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