Conformal invariants of twisted Dirac operators and positive scalar curvature
Date
2013
Authors
Bernameur, M.
Varghese, M.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Journal of Geometry and Physics, 2013; 70:39-47
Statement of Responsibility
Moulay Tahar Benameur, Varghese Mathai
Conference Name
Abstract
For a closed, spin, odd dimensional Riemannian manifold (Y, g) , we define the rho invariant ρspin(Y,E,H,[g]) for the twisted Dirac operator ∂<sup>E</sup>HE on Y, acting on sections of a flat Hermitian vector bundle E over Y, where H = ∑ <sup>i j +1</sup><inf>H2j +1</inf> is an odd-degree closed differential form on Y and <inf>H2j +1</inf> is a real-valued differential form of degree 2j + 1. We prove that it only depends on the conformal class [g] of the metric g. In the special case when H is a closed 3-form, we use a Lichnerowicz-Weitzenböck formula for the square of the twisted Dirac operator, which in this case has no first order terms, to show that ρspin(Y,E,H,[g])=ρspin(Y,E,[g]) for all {pipe}H {pipe} small enough, whenever g is conformally equivalent to a Riemannian metric of positive scalar curvature. When H is a top-degree form on an oriented three dimensional manifold, we also compute ρspin(Y,E,H). © 2013 Elsevier B.V.
School/Discipline
Dissertation Note
Provenance
Description
Access Status
Rights
© 2013 Elsevier B.V. All rights reserved.