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Characteristic Classes

In: Supersymmetry and Equivariant de Rham Theory

Author

Listed:
  • Victor W. Guillemin

    (Massachusetts Institute of Technology, Department of Mathematics)

  • Shlomo Sternberg

    (Harvard University, Department of Mathematics)

  • Jochen Brüning

    (Humboldt-Universität Berlin, Institut für Mathematik Mathematisch-Naturwissenschaftliche Fakultät II)

Abstract

Recall from section 4.5 that if A is a G* module, then we have a characteristic homomorphism $${k_*}:S{({g^*})^G} \to {H_G}(A),$$ and that the elements of the image of k * are known as characteristic classes. But we have not really written down what the ring S (g*) G is for any group G. The main function of this chapter is to remedy this by summarizing standard computations of S (g*) G for various important groups. Suppose that: ø : K → G is a Lie group homomorphism, and let k denote the Lie algebra of K. The induced Lie algebra map k → g dualizes to a map g* → k* which extends to an algebra homomorphism S(g*)G → S(k*)k. We will examine this homomorphism for various examples of inclusions of classical groups.

Suggested Citation

  • Victor W. Guillemin & Shlomo Sternberg & Jochen Brüning, 1999. "Characteristic Classes," Springer Books, in: Supersymmetry and Equivariant de Rham Theory, chapter 0, pages 95-110, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-03992-2_8
    DOI: 10.1007/978-3-662-03992-2_8
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