On Formality of Some Homogeneous Spaces
Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710 Olsztyn, Poland
Received: 17 July 2019 / Revised: 31 July 2019 / Accepted: 2 August 2019 / Published: 5 August 2019
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Abstract Let be a homogeneous space of a compact simple classical Lie group G. Assume that the maximal torus of H is conjugate to a torus whose Lie algebra is the kernel of the maximal root of the root system of the complexified Lie algebra . We prove that such homogeneous space is formal. As an application, we give a short direct proof of the formality property of compact homogeneous 3-Sasakian spaces of classical type. This is a complement to the work of Fernández, Muñoz, and Sanchez which contains a full analysis of the formality property of -bundles over the Wolf spaces and the proof of the formality property of homogeneous 3-Sasakian manifolds as a corollary.
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MDPI and ACS Style
Tralle, A. On Formality of Some Homogeneous Spaces. Symmetry 2019, 11, 1011.
Tralle A. On Formality of Some Homogeneous Spaces. Symmetry. 2019; 11(8):1011.
Tralle, Aleksy. 2019. "On Formality of Some Homogeneous Spaces." Symmetry 11, no. 8: 1011.
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