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A vanishing theorem in twisted de Rham cohomology

Part of: General theory of differentiable manifolds Global differential geometry

Published online by Cambridge University Press:  20 March 2013

Ana Cristina Ferreira
Ana Cristina Ferreira*
Affiliation:
Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710057 Braga, Portugal (anaferreira@math.uminho.pt)
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Abstract

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We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

Keywords

twisted de Rham cohomologyconnections with skew torsionDirac operators

MSC classification

Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 58A14: Hodge theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 2 , June 2013 , pp. 501 - 508
Copyright
Copyright © Edinburgh Mathematical Society 2013

References

1.Agricola, I. and Friedrich, T., On the holonomy of connections with skew-symmetric torsion, Math. Annalen 328 (2004), 711–748.CrossRefGoogle Scholar
2.Atiyah, M., K-theory past and present, Proceedings of the Berlin Mathematical Society, pp. 411–417 (Berliner Mathematische Gesellschaft, Berlin, 2001).Google Scholar
3.Atiyah, M. and Segal, G., Twisted K-theory and cohomology, Nankai Tracts in Mathematics, Volume 11, pp. 5–43 (World Scientific, 2006).Google Scholar
4.Bismut, J. M., A local index theorem for non-Kähler manifolds, Math. Annalen 284 (1989), 681–699.CrossRefGoogle Scholar
5.Bouwknegt, P., Carey, A., Mathai, V., Murry, M. and Stevenson, D., Twisted K-theory and K-theory of bundle gerbes, Commun. Math. Phys. 228 (2002), 17–45.CrossRefGoogle Scholar
6.Bouwknegt, P., Evslin, J. and Mathai, V., T-duality: topology change from H-flux, Commun. Math. Phys. 249 (2004), 383–415.CrossRefGoogle Scholar
7.Cavalcanti, G., New aspect of the dd c-lemma, DPhil. Thesis, University of Oxford (2004).Google Scholar
8.Kobayashi, S. and Nomizu, K., Foundations of differentiable geometry, Volumes I and II (Interscience, New York, 1969).Google Scholar
9.Kosmann-Schwarzbach, Y., Derived brackets, Lett. Math. Phys. 69 (2004), 61–87.CrossRefGoogle Scholar
10.Lawson, H. B. and Michelsohn, M. L., Spin geometry (Princeton University Press, 1989).Google Scholar
11.Mathai, V. and Wu, S., Analytic torsion for twisted de Rham complexes, Diff. Geom. 88 (2011), 297–332.Google Scholar
12.Rohm, R. and Witten, E., The antisymmetric tensor field in superstring theory, Annals Phys. 170 (1986), 454–489.CrossRefGoogle Scholar
13.Roytenberg, D., Courant algebroids, derived brackets and even symplectic supermani-folds, PhD Thesis, University of California, Berkeley (1999).Google Scholar
14.Ševera, P. and Weinstein, A., Poisson geometry with a 3-form background, Prog. Theor. Phys. Suppl. 144 (2001), 145–154.CrossRefGoogle Scholar