Geodesic
On Morse theory for manifolds with cross products
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 456-459

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We consider the finite-dimensional Morse theory for closed Riemannian manifolds equipped with the vector cross product on the tangent bundle. These are, for example, $G_2$-manifolds. Under some conditions toric actions generate the Morse–Bott function, whose gradient trajectories are explicit. This allows us to construct the Morse–Bott complex and calculate the real cohomology ring of the manifold.
Keywords: Morse theory, toric action. 
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     author = {D. V. Egorov},
     title = {On {Morse} theory for manifolds with cross products},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {456--459},
     publisher = {mathdoc},
     volume = {9},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2012_9_a14/}
}
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D. V. Egorov. On Morse theory for manifolds with cross products. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 456-459. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a14/