Rational homotopy of a map of projective quaternions and their relative Gottlieb groups. (English) Zbl 07892368
Summary: In this paper, we show in terms of Sullivan models that the rational homotopy of a map \(\iota:\mathbb{H} P^m\hookrightarrow\mathbb{H} P^{m+r}\) between projective quaternion spaces is a product of a quaternion projective space and odd spheres. We also study the properties of a map \(\operatorname{aut}_1\mathbb{H} P^m\rightarrow\mathrm{maps} (\mathbb{H} P^m,\mathbb{H} P^{m+r};\iota)\) and its \(G\)-sequence.
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