Rational homotopy type of mapping spaces between complex projective spaces and their evaluation subgroups
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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.
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.
참고문헌 (17)
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