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

Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 259-267 https://doi.org/10.4134/CKMS.c200431 Published online August 9, 2021 Printed January 31, 2022

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 $ \aut_1 \mathbb{C}P^n \rightarrow \map ( \mathbb{C}P^n, \mathbb{C}P^{n+k}; i_{n,k}) $ and the resulting $G$-sequence.