Quaternionic projective space: Difference between revisions

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==Quaternionic projective plane==

The 8-dimensional '''H'''''P''<supmath>''\mathbb{HP}^{2''}</supmath> has a [[circle action]], by the group of complex scalars of absolute value 1 acting on the other side (so on the right, as the convention for the action of ''c'' above is on the left). Therefore the [[quotient manifold]]

<math>\mathbb{HP}^{2}/\mathrm{U}(1)</math>

:'''H'''''P''^''2''/''U''(1)

may be taken, writing [[U(1)]] for the [[circle group]]. It has been shown that this quotient is the 7-[[sphere]], a result of [[Vladimir Arnold]] from 1996, later rediscovered by [[Edward Witten]] and [[Michael Atiyah]].