On Elliptic Genera and Theta-Functions

  title={On Elliptic Genera and Theta-Functions},
  author={Kefeng Liu},
The main purpose of this paper is to give a simple and unified new proof of the Witten rigidity theorems, which were conjectured by Witten and first proved by Taubes [T], Bott-Taubes [BT], Hirzebruch [H] and Krichever [Kr]. Our proof shows that the modular invariance, which is the intrinsic symmetry of elliptic genera, actually implies their rigidity. Some new properties of elliptic genera and their relationships with theta-functions are also discussed. We remark that our proof makes essential… CONTINUE READING
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