Geometriae Dedicata

, Volume 35, Issue 1–3, pp 309–343 | Cite as

Elliptic genera, involutions, and homogeneous spin manifolds

  • F. Hirzebruch
  • P. Slodowy


We study the normalized elliptic genera Φ(X)=ϕ(X)/εk/2 for 4k-dimensional homogeneous spin manifolds X and show that they are constant as modular functions. The basic tool is a reduction formula relating Φ(X) to that of the self-intersection of the fixed point set of an involution γ on X. When Φ(X) is a constant it equals the signature of X. We derive a general formula for sign(G/H), GH compact Lie groups, and determine its value in some cases by making use of the theory of involutions in compact Lie groups.


General Formula Basic Tool Modular Function Elliptic Genus Spin Manifold 
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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • F. Hirzebruch
    • 1
  • P. Slodowy
    • 2
  1. 1.Max-Planck-Institut für MathematikBonn 3Germany
  2. 2.Mathematisches Institut BUniversität StuttgartStuttgart 80Germany

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