Rational homotopy of a map of projective quaternions and their relative Gottlieb groups

Document Type : Original Article

Author

Oteng Maphane

Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana

10.22034/kjm.2024.409622.2950

Abstract

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 ${\rm aut}_{1}\mathbb H P^{m}\rightarrow{\rm maps} (\mathbb H P^{m},\mathbb H P^{m+r};\iota) $ and its $G$-sequence. 

Keywords

Evaluation subgroups

$L_{\infty} $ algebra

mapping spaces

Subjects

• 55 Algebraic topology

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