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
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.
Keywords : Rational homotopy theory, mapping space, $L_{\infty}$ algebra
MSC numbers : Primary 55P62; Secondary 54C35
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