Mathematical Research Letters
Volume 8 (2001)
On Elliptic Genera and Foliations
Pages: 361 – 376
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.