English

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

Differential Geometry 2019-02-23 v1

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 dcd^c and the Dolbeault cohomologies in K\"ahler geometry, and assigns an LL_\infty-algebra to each associative submanifold. We provide several concrete computations of the Fr\"olicher-Nijenhuis cohomology.

Keywords

Cite

@article{arxiv.1810.12714,
  title  = {Fr\"olicher-Nijenhuis bracket on manifolds with special holonomy},
  author = {Kotaro Kawai and Hông Vân Lê and Lorenz Schwachhöfer},
  journal= {arXiv preprint arXiv:1810.12714},
  year   = {2019}
}

Comments

14 pages, To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics". arXiv admin note: text overlap with arXiv:1703.05133