Abstract
We construct an explicit deformation retraction of the manifold of symplectic flags onto the manifold of complex flags. The main tool is the polar decomposition of symplectic matrices. We also give a new definition of symplectic Stiefel manifold and prove that it has the same homotopy type as the complex Stiefel manifold.
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Ajayi, D.O.A., Banyaga, A. An explicit retraction of symplectic flag manifolds onto complex flag manifolds. J. Geom. 104, 1–9 (2013). https://doi.org/10.1007/s00022-013-0148-4
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DOI: https://doi.org/10.1007/s00022-013-0148-4