Mathematical Research Letters

Volume 8 (2001)

Number 3

On Elliptic Genera and Foliations

Pages: 361 – 376



Kefeng Liu (University of California at Los Angeles)

Xiaonan Ma (Institut für Mathematik)

Weiping Zhang (Nankai University)


We prove several vanishing theorems for a class of generalized elliptic genera on foliated manifolds, by using classical equivariant index theory. The main techniques are the use of the Jacobi theta-functions and the construction of a new class of elliptic operators associated to foliations.

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