Mapping spaces between manifolds and the evaluation map

Felix, Yves

doi:10.1090/S0002-9939-2011-10763-9

Mapping spaces between manifolds and the evaluation map
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by Yves Felix PDF

Proc. Amer. Math. Soc. 139 (2011), 3763-3768 Request permission

Abstract:

Let $f : M\to N$ be a map between simply connected $n$-dimensional manifolds. We suppose that deg$f\neq 0$. Then the injection of $aut_1(N)$ into the component $\mbox {Map} (M,N;f)$ of the mapping space containing $f$ induces an injection on the rational homotopy groups, and the evaluation at the base point $\mbox {map}(M,N;f)\to N$ is zero on the rational homotopy groups of even dimension.

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