Groupoids and an index theorem for conical pseudo-manifolds
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Claire Debord
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 new ingredient in our proof is a non-commutative algebra that plays in our setting the role of 𝒞0(T*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.
© Walter de Gruyter Berlin · New York 2009
Articles in the same Issue
- Groupoids and an index theorem for conical pseudo-manifolds
- Linear forms in elliptic logarithms
- Random quotients of the modular group are rigid and essentially incompressible
- The pro-p Hom-form of the birational anabelian conjecture
- Multiplication operators on the Bergman space via the Hardy space of the bidisk
- Morita equivalences of cyclotomic Hecke algebras of type G(r, p, n)
- Special correspondences and Chow traces of Landweber-Novikov operations
- Double Kodaira fibrations
Articles in the same Issue
- Groupoids and an index theorem for conical pseudo-manifolds
- Linear forms in elliptic logarithms
- Random quotients of the modular group are rigid and essentially incompressible
- The pro-p Hom-form of the birational anabelian conjecture
- Multiplication operators on the Bergman space via the Hardy space of the bidisk
- Morita equivalences of cyclotomic Hecke algebras of type G(r, p, n)
- Special correspondences and Chow traces of Landweber-Novikov operations
- Double Kodaira fibrations
