Communications of the
Korean Mathematical Society CKMS

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 ightarrow 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