English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper is a first of a series of three papers which study eta invariantsfor laminations. In this first paper, we extend the results of Higson and Roeto deal with regular (unbounded) operators and more importantly to take intoaccount Morita equivalence of underlying $C^*$-algebras. Given an orientedleafwise map between leafwise oriented laminations on compact spaces,satisfying some natural assumptions, we construct a pull-back morphism betweenthe de Rham HP complexes and prove their expected functoriality. As abyproduct, when two leafwise oriented laminations are leafwise homotopyequivalent, our construction allows to deduce an explicit path joining theleafwise signature operators and hence the famous Large Time Path appearing inthe proof of the homotopy invariance of the measured Cheeger-Gromov number.

Leafwise homotopies and Hilbert-Poincare complexes. I. Regular HP-complexes and leafwise pull-back maps