Groupoids and an index theorem for conical pseudo-manifolds

Abstract

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, compact manifold $M$. A main ingredient is a non-commutative algebra that plays in our setting the role of $C_0(T^{\ast }M)$. We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in $K$-theory. We then give a new proof of the Atiyah-Singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds.

References in corpus (2)

• On the Homotopy Classification of Elliptic Operators on Manifolds with Edges
• Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds

Cited by in corpus (1)

• Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds