Maps from Grassmannians of 2-planes to projective spaces

2025/01/23 by Brasil, Ricardo, Ana Cristina Ferreira, Ferreira, Ana Cristina +2
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2501.13590

Abstract

Using quaternions and octonions, we construct some maps from the Grassmannian of 2-dimensional planes of ℝⁿ, Gr₂(ℝⁿ), to the projective space ℝP^k, for certain values of n and k. All of our maps induce an isomorphism at the level of fundamental groups, and two of them are shown to be submersions. As an application, we obtain new estimates of the Lusternik-Schnirelmann category of Gr₂(ℝⁿ) for specific values of n.

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