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arXiv · 1810.12714

Fr\"olicher-Nijenhuis bracket on manifolds with special holonomy

Kotaro Kawai·Hông Vân Lê·Lorenz Schwachhöfer
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Abstract

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.

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Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer. 2018-10-30. Fr\"olicher-Nijenhuis bracket on manifolds with special holonomy. https://arxiv.org/abs/1810.12714

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