Interior Kasparov product for $\varrho$-classes on Riemannian foliated bundles

DOI10.1016/J.JFA.2023.109863arXiv2201.10616MaRDI QIDQ6389184

Publication date: 25 January 2022

Abstract: Let

i o t a c o l o n m a t h c a l F_{0} o m a t h c a l F_{1}

be a suitably oriented inclusion of foliations over a manifold

M

, then we extend the construction of the lower shriek maps given by Hilsum and Skandalis to adiabatic deformation groupoid C*-algebras: we construct an asymptotic morphism

(i o t a_{a d}^{[0, 1)})_{!} i n E_{n} l e f t (C^{*} (G_{a d}^{[0, 1)}), C^{*} (H_{a d}^{[0, 1)}) i g h t)

, where

G

and

H

are the monodromy groupoids associated with

m a t h c a l F_{0}

and

m a t h c a l F_{1}

respectively. Furthermore, we prove an interior Kasparov product formula for foliated

v a r r h o

-classes associated with longitudinal metrics of positive scalar curvature in the case of Riemannian foliated bundles.

Mathematics Subject Classification ID

Foliations (differential geometric aspects) (53C12) Kasparov theory ((KK)-theory) (19K35) Topological groupoids (including differentiable and Lie groupoids) (22A22)

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