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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.
##### MSC:
 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