Mapping spaces between manifolds and the evaluation map
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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.References
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Additional Information
- Yves Felix
- Affiliation: Institut Mathematique, Université Catholique de Louvain, 2, Chemin du Cyclotron, 1348 Louvain-La-Neuve, Belgium
- Received by editor(s): July 17, 2010
- Received by editor(s) in revised form: August 16, 2010, and August 24, 2010
- Published electronically: February 17, 2011
- Communicated by: Brooke Shipley
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 3763-3768
- MSC (2010): Primary 55P62; Secondary 55Q52
- DOI: https://doi.org/10.1090/S0002-9939-2011-10763-9
- MathSciNet review: 2813406