Index, eta and rho-invariants on foliated bundles

Details Index, eta and rho-invariants on foliated bundles Index, eta and rho-invariants on foliated bundles

2008-09-12

arxiv.org/abs/0809.2268v1

Mathematics

Differential Geometry

65 pages

Scientific paper

We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator $D_m$ on the maximal Connes-Skandalis Hilbert module and explain how the functional calculus of $D_m$ encodes both the leafwise calculus and the monodromy calculus in the corresponding von Neumann algebras. When the foliation is endowed with a holonomy invariant transverse measure, we explain the compatibility of various traces and determinants. We extend Atiyah's index theorem on Galois coverings to these foliations. We define a foliated rho-invariant and investigate its stability properties for the signature operator. Finally, we establish the foliated homotopy invariance of such a signature rho-invariant under a Baum-Connes assumption, thus extending to the foliated context results proved by Neumann, Mathai, Weinberger and Keswani on Galois coverings.

Affiliated with

Also associated with

No associations

Rating

Index, eta and rho-invariants on foliated bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Index, eta and rho-invariants on foliated bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Index, eta and rho-invariants on foliated bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-369853