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Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces
Enrique Mac\'ias-Virg\'os, Daniel Tanr\'e
https://arxiv.org/abs/2509.20210 https…

Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces
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. Fernández-Suárez, A. Gómez-Tato and D. Tanré) and has to be compared to the equali…