The Crowley-Nordström invariants of $G_2$-Structures on Aloff--Wallach Spaces

Artem Aleshin

We study homogeneous $G_2$-structures on the Aloff-Wallach spaces $N_{k,l}=SU(3)/S_{k,l}^1,$ and compute the Crowley--Nordström invariants associated to these structures. In the ca…