Index, eta and rho-invariants on foliated bundles

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dc.creatorBenameur, Moulay-Tahar
dc.creatorPiazza, Paolo
dc.date2008-09-12
dc.date.accessioned2026-07-07T10:02:35Z
dc.date.available2026-07-07T10:02:35Z
dc.descriptionWe 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.
dc.description65 pages
dc.identifierhttps://arxiv.org/abs/0809.2268
dc.identifierhttp://arxiv.org/abs/0809.2268
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169023
dc.subjectDifferential Geometry
dc.subjectK-Theory and Homology
dc.subject58J20; 58J22
dc.titleIndex, eta and rho-invariants on foliated bundles
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