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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2012, Volume 9, Pages 456–459
(Mi semr377)
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Geometry and topology
On Morse theory for manifolds with cross products
D. V. Egorov Ammosov Northeastern federal university,
Kulakovsky str. 48, 677000, Yakutsk, Russia
Abstract:
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.
Received April 2, 2012, published October 19, 2012
Citation:
D. V. Egorov, “On Morse theory for manifolds with cross products”, Sib. Èlektron. Mat. Izv., 9 (2012), 456–459
Linking options:
https://www.mathnet.ru/eng/semr377 https://www.mathnet.ru/eng/semr/v9/p456
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Abstract page: | 179 | Full-text PDF : | 52 | References: | 50 |
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