Abstract
In this article, we summarize our recent results on the study of manifolds with special holonomy via the Frölicher–Nijenhuis bracket. This bracket enables us to define the Frölicher–Nijenhuis cohomologies which are analogues of the \(d^c\) and the Dolbeault cohomologies in Kähler geometry, and assigns an \(L_\infty \)-algebra to each associative submanifold. We provide several concrete computations of the Frölicher–Nijenhuis cohomology.
The first named author is supported by JSPS KAKENHI Grant Numbers JP17K14181, and the research of the second named author was supported by the GAČR project 18-00496S and RVO:67985840. The third named author was supported by the Deutsche Forschungsgemeinschaft by grant SCHW 893/5-1.
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Kawai, K., Vân Lê, H., Schwachhöfer, L. (2020). Frölicher–Nijenhuis Bracket on Manifolds with Special Holonomy. In: Karigiannis, S., Leung, N., Lotay, J. (eds) Lectures and Surveys on G2-Manifolds and Related Topics. Fields Institute Communications, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0577-6_8
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DOI: https://doi.org/10.1007/978-1-0716-0577-6_8
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