Constructs C*-algebra from pseudodifferential operators and partial group actions on blown-up manifold Y, classifies elliptic elements as K0(C0(T*Y°) ⋊ Γ) ⊕ K0(C(∂Y) ⋊ Γ) with index contribution only from first summand for polynomial-growth groups.
An equivariant index theorem for hypoelliptic operators
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abstract
Let M be a foliated manifold and G a discrete group acting on M by diffeomorphisms mapping leaves to leaves. Then G naturally acts by automorphisms on the algebra of Heisenberg pseudodifferential operators on the foliation. Our main result is an index theorem for hypoelliptic-type operators which belong to the crossed product of the Heisenberg pseudodifferential operators with the group G. As a corollary, we get a solution to Connes-Moscovici's transverse problem in arbitrary codimensions, by exhibiting an explicit formula in terms of characteristic classes of equivariant vector bundles over M, for the Chern-Connes character associated to their hypoelliptic signature operator.
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2026 1verdicts
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Elliptic Boundary Value Problems and Partial Group Actions
Constructs C*-algebra from pseudodifferential operators and partial group actions on blown-up manifold Y, classifies elliptic elements as K0(C0(T*Y°) ⋊ Γ) ⊕ K0(C(∂Y) ⋊ Γ) with index contribution only from first summand for polynomial-growth groups.