Related papers: A topological index theorem for manifolds with cor…

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth,…

The paper is devoted to the index theory of orbital and transverse elliptic operators on manifolds with a proper Lie group action. It corrects errors of my previous paper (published in JNCG in 2016) on transverse operators and contains new…

We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the…

This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry.

Roe's partitioned manifold index theorem applies when a complete Riemannian manifold $M$ is cut into two pieces along a compact hypersurface $N$. It states that a version of the index of a Dirac operator on $M$ localized to $N$ equals the…

We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show…

We present an index theorem for certain hypoelliptic differential operators on foliated manifolds. Our proof is a development of Alain Connes tangent groupoid proof of the Atiyah-Singer index theorem. The paper is largely self-contained.

We study twisted $Spin^c$-manifolds over a paracompact Hausdorff space $X$ with a twisting $\alpha: X \to K(\ZZ, 3)$. We introduce the topological index and the analytical index on the bordism group of $\alpha$-twisted $Spin^c$-manifolds…

We introduce and study the index morphism for G-invariant leafwise G-transversally elliptic operators on smooth closed foliated manifolds which are endowed with leafwise actions of the compact group G. We prove the usual axioms of excision,…

Many index theorems (both classical and in noncommutative geometry) can be interpreted in terms of a Lie groupoid acting properly on a manifold and leaving an elliptic family of pseudodifferential operators invariant. Alain Connes in his…

Many index theorems (both classical and in noncommutative geometry) can be interpreted in terms of a Lie groupoid acting properly on a manifold and leaving an elliptic family of pseudodifferential operators invariant. Alain Connes in his…

This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order…

We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := D+ V, where D is a Dirac operators and V is an unbounded potential at infinity on a possibly…

Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…

We generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators. The generalization will follow from a local index theorem that is valid on any…

An analytic index is defined for a family of cusp pseudodifferential operators, $P_b,$ on a fibration with fibres which are compact manifolds with boundaries, provided the family is elliptic and has invertible indicial family at the…

An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is…

We introduce a simplified (coarse) version of pseudo-differential calculus for operators of order zero on complete Riemannian manifolds. This calculus works for the usual Hormander (1,0) class of operators, as well as for…

This paper provides an E-theoretic proof of an exact form, due to E. Troitsky, of the Mischenko-Fomenko Index Theorem for elliptic pseudodifferential operators over a unital C*-algebra. The main ingredients in the proof are the use of…

We develop elliptic theory of operators associated with a diffeomorphism of a closed smooth manifold. The aim of the present paper is to obtain an index formula for such operators in terms of topological invariants of the manifold and of…