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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

This paper is the the third part of a series of paper whose aim is to use ofthe framework of \emph{twisted spectral triples} to study conformal geometryfrom a noncommutive geometric viewpoint. In this paper we reformulate theinequality of Vafa-Witten \cite{VW:CMP84} in the setting of twisted spectraltriples. This involves a notion of Poincar\'e duality for twisted spectraltriples. Our main results have various consequences. In particular, we obtain aversion in conformal geometry of the original inequality of Vafa-Witten, in thesense of an explicit control of the Vafa-Witten bound under conformal changesof metric. This result has several noncommutative manifestations for conformaldeformations of ordinary spectral triples, spectral triples associated toconformal weights on noncommutative tori, and spectral triples associated toduals of torsion-free discrete cocompact subgroups satisfying the Baum-Connesconjecture.

Noncommutative Geometry and Conformal Geometry. III. Vafa-Witten Inequality and Poincar\'e Duality