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The index of quantized contact transformations on manifolds with conical singularities. (English. Russian original) Zbl 1072.58502
Dokl. Math. 60, No. 2, 243-245 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 368, No. 5, 598-600 (1999).
From the text: In this announcement the authors give a formula for the index of the Fourier integral operator \(T\) associated to a contact transformation of the cosphere bundle of a manifold \(M\) with conical singularities provided symmetry conditions hold allowing to extend \(T\) to the double of \(M\). Then a combination of the Epstein-Melrose formula with a relative index theorem leads to the index formula.
58J20 Index theory and related fixed-point theorems on manifolds
35S30 Fourier integral operators applied to PDEs
58J40 Pseudodifferential and Fourier integral operators on manifolds