A symbol calculus for foliations

DOI10.4171/JNCG/11-3-11arXiv1511.05697MaRDI QIDQ6267523

James L. Heitsch, Moulay-Tahar Benameur

Publication date: 18 November 2015

Abstract: The classical Getzler rescaling theorem is extended to the transverse geometry of foliations. More precisely, a Getzler rescaling calculus, as well as a Block-Fox calculus of asymptotic operators, is constructed for all transversely spin foliations. This calculus applies to operators of degree $m$ globally times degree $ell$ in the leaf directions, and is thus an appropriate tool for a better understanding of the index theory of transversely elliptic operators on foliations. The main result is that the composition of A$Psi$DOs is again an A$Psi$DO, and includes a formula for the leading symbol.

Mathematics Subject Classification ID

Foliations (differential geometric aspects) (53C12) Pseudodifferential operators (47G30)

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