Lefschetz fixed point theorem for quantized canonical transformations (Q1966236)

The authors prove a fixed point theorem for a trace-class Fourier integral operator associated with a quantized canonical transformation of a closed manifold cotangent space. Their analysis of the leading term of the asymptotic trace formula reveals the term dependence on the transformation fixed points. With reference to reasoning by \textit{B. V. Fedosov} [in: Partial differential equations VIII. Encycl. Math. Sci. 65, 155-251 (1996; Zbl 0884.58087)], the authors show that their result generalizes the Atiyah-Bott-Lefschetz fixed point theorem.