Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer
Published 2018-10-30Version 1
In this article, we summarize our recent results on the study of manifolds with special holonomy via the Fr\"olicher-Nijenhuis bracket. This bracket enables us to define the Fr\"olicher-Nijenhuis cohomologies which are analogues of the $d^c$ and the Dolbeault cohomologies in K\"ahler geometry, and assigns an $L_\infty$-algebra to each associative submanifold. We provide several concrete computations of the Fr\"olicher-Nijenhuis cohomology.
Comments: 14 pages, To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"
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