Antonini, Paolo (2013) The Atiyah-Patodi-Singer index formula for measured foliations. BULLETIN DES SCIENCES MATHEMATIQUES, 137 (2). pp. 140-176. ISSN 0007-4497,
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Let X-0 be a compact Riemannian manifold with boundary endowed with an oriented, measured even dimensional foliation with purely transverse boundary. Let X be the manifold with cylinder attached and extended foliation. We prove that the L-2-measured index of a Dirac type operator is well defined and the following Atiyah-Patodi-Singer index formula is true ind(L2,Lambda) (D+) = <(A) over cap (X, del) Ch(E/S), C-Lambda > + 1/2[eta(Lambda)(D-F partial derivative) - h(Lambda)(+) + h(Lambda)(-)] Here Lambda is a holonomy invariant transverse measure, eta(Lambda)(D-F partial derivative) is the Ramachandran eta invariant (M. Ramachandran, 1993) [23] of the leafwise boundary operator and the Lambda-dimensions h(Lambda)(+/-) of the space of the limiting values of extended solutions is suitably defined using square integrable representations of the equivalence relation of the foliation with values on weighted Sobolev spaces on the leaves. (C) 2010 Published by Elsevier Masson SAS.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE PROPAGATION SPEED; VON-NEUMANN-ALGEBRAS; ETA-INVARIANTS; DIRAC OPERATORS; MANIFOLDS; GEOMETRY; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Apr 2020 10:37 |
| Last Modified: | 23 Apr 2020 10:37 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17019 |
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