Spectral sections, twisted rho invariants and positive scalar curvature

  • Moulay-Tahar Benameur

    Université Montpellier 2, France
  • Varghese Mathai

    University of Adelaide, Australia


We had previously defined in [10], the rho invariant for the twisted Dirac operator on a closed odd dimensional Riemannian spin manifold , acting on sections of a flat hermitian vector bundle over , where is an odd-degree differential form on and is a real-valued differential form of degree . Here we show that it is a conformal invariant of the pair . In this paper we express the defect integer in terms of spectral flows and prove that , whenever is a Riemannian metric of positive scalar curvature. In addition, if the maximal Baum–Connes conjecture holds for (which is assumed to be torsion-free), then we show that for all , significantly generalizing results in [10]. These results are proved using the Bismut–Weitzenböck formula, a scaling trick, the technique of noncommutative spectral sections, and the Higson–Roe approach [22].

Cite this article

Moulay-Tahar Benameur, Varghese Mathai, Spectral sections, twisted rho invariants and positive scalar curvature. J. Noncommut. Geom. 9 (2015), no. 3, pp. 821–850

DOI 10.4171/JNCG/209