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arXiv · 2509.20210

Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces

Enrique Macías-Virgós·Daniel Tanré
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Abstract

Let $Q_n$ be the quasi-projective subspace of the symplectic group $\mathrm{Sp}(n)$. In this short note, we prove that the subspace Lusternik-Schnirelmann category of $Q_n$ in $\mathrm{Sp}(n)$ is 2. For that, we use a quaternionic logarithm, as Singhof did in the complex case for the determination of the Lusternik-Schnirelmann category of the unitary group. Our result generalizes the known case $n=2$ (by L. Fern\'andez-Su\'arez, A. G\'omez-Tato and D. Tanr\'e) and has to be compared to the equality $\mathrm{cat}\,Q_{3}=3$, established by N. Iwase and T. Miyauchi.

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Enrique Macías-Virgós, Daniel Tanré. 2025-09-24. Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces. https://arxiv.org/abs/2509.20210

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