Memoirs of the American Mathematical Society 1994; 88 pp; softcover Volume: 110 ISBN10: 0821825909 ISBN13: 9780821825907 List Price: US$37 Individual Members: US$22.20 Institutional Members: US$29.60 Order Code: MEMO/110/528
 This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higherdegree analogues of the Fröhlich spinor class, which quantify the difference between the StiefelWhitney classes of an orthogonal representation and the HasseWitt classes of the associated form. Jardine establishes various basic properties, including vanishing in odd degrees and an induction formula for quadratic field extensions. The methods used include the homotopy theory of simplicial presheaves and the action of the Steenrod algebra on mod 2 étale cohomology. Readership Research mathematicians, graduate students. Table of Contents  Introduction
 The operation \(P_2\)
 The cohomology of \(BO_n\)
 The cohomological induction formula
 Higher spinor classes
 References
