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- W2040894951 abstract "This paper is the the third part of a series of paper whose aim is to use of the framework of emph{twisted spectral triples} to study conformal geometry from a noncommutive geometric viewpoint. In this paper we reformulate the inequality of Vafa-Witten cite{VW:CMP84} in the setting of twisted spectral triples. This involves a notion of Poincar'e duality for twisted spectral triples. Our main results have various consequences. In particular, we obtain a version in conformal geometry of the original inequality of Vafa-Witten, in the sense of an explicit control of the Vafa-Witten bound under conformal changes of metric. This result has several noncommutative manifestations for conformal deformations of ordinary spectral triples, spectral triples associated to conformal weights on noncommutative tori, and spectral triples associated to duals of torsion-free discrete cocompact subgroups satisfying the Baum-Connes conjecture." @default.
- W2040894951 created "2016-06-24" @default.
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- W2040894951 date "2015-02-01" @default.
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- W2040894951 title "Noncommutative geometry and conformal geometry. III. Vafa–Witten inequality and Poincaré duality" @default.
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- W2040894951 doi "https://doi.org/10.1016/j.aim.2014.12.009" @default.
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