Rational homotopy type of mapping spaces between complex projective spaces and their evaluation subgroups

Commun. Korean Math. Soc. Published online August 9, 2021

Jean Baptiste Gatsinzi
Botswana International University of Science and Technology

Abstract : We use $L_{\infty}$ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion $i_{n,k}: \mathbb{C}P^n \hookrightarrow \mathbb{C}P^{n+k}$ between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping $ \mathrm{aut}_1 \mathbb{C}P^n \rightarrow \mathrm{map}( \mathbb{C}P^n, \mathbb{C}P^{n+k}; i_{n,k}) $ and the resulting $G$-sequence.