Conformal invariants of twisted Dirac operators and positive scalar curvature
| dc.contributor.author | Bernameur, M. | |
| dc.contributor.author | Varghese, M. | |
| dc.date.issued | 2013 | |
| dc.description.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. | |
| dc.description.statementofresponsibility | Moulay Tahar Benameur, Varghese Mathai | |
| dc.identifier.citation | Journal of Geometry and Physics, 2013; 70:39-47 | |
| dc.identifier.doi | 10.1016/j.geomphys.2013.03.010 | |
| dc.identifier.issn | 0393-0440 | |
| dc.identifier.orcid | Varghese, M. [0000-0002-1100-3595] | |
| dc.identifier.uri | http://hdl.handle.net/2440/79785 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier Science BV | |
| dc.relation.grant | ARC | |
| dc.rights | © 2013 Elsevier B.V. All rights reserved. | |
| dc.source.uri | https://doi.org/10.1016/j.geomphys.2013.03.010 | |
| dc.subject | Twisted Dirac rho invariant | |
| dc.subject | Twisted Dirac eta invariant | |
| dc.subject | Conformal invariants | |
| dc.subject | Twisted Dirac operator | |
| dc.subject | Positive scalar curvature | |
| dc.subject | Manifolds with boundary | |
| dc.title | Conformal invariants of twisted Dirac operators and positive scalar curvature | |
| dc.type | Journal article | |
| pubs.publication-status | Published |