Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668920 | Bulletin des Sciences Mathématiques | 2013 | 37 Pages |
Abstract
Let X0 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 L2-measured index of a Dirac type operator is well defined and the following Atiyah-Patodi-Singer index formula is trueindL2,Î(D+)=ãAË(X,â)Ch(E/S),CÎã+1/2[ηÎ(DFâ)âhÎ++hÎâ]. Here Î is a holonomy invariant transverse measure, ηÎ(DFâ) is the Ramachandran eta invariant (M. Ramachandran, 1993) [23] of the leafwise boundary operator and the Î-dimensions hα 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Paolo Antonini,