Back to Search
Start Over
Noncommutative geometry and conformal geometry. III. Vafa–Witten inequality and Poincaré duality
- Source :
- Advances in Mathematics. 272:761-819
- Publication Year :
- 2015
- Publisher :
- Elsevier BV, 2015.
-
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.<br />Comment: Final version. 38 pages
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
General Mathematics
Mathematics - Operator Algebras
Conformal map
Noncommutative geometry
Algebra
symbols.namesake
Mathematics::K-Theory and Homology
Conformal symmetry
symbols
Noncommutative algebraic geometry
Noncommutative quantum field theory
Mathematics::Symplectic Geometry
Spectral triple
Conformal geometry
Poincaré duality
Mathematics
Subjects
Details
- ISSN :
- 00018708
- Volume :
- 272
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematics
- Accession number :
- edsair.doi.dedup.....7df4941be776bca0f3daf270fdfc84cd