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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Mapping spaces between manifolds and the evaluation map

Author: Yves Felix
Journal: Proc. Amer. Math. Soc. 139 (2011), 3763-3768
MSC (2010): Primary 55P62; Secondary 55Q52
Published electronically: February 17, 2011
MathSciNet review: 2813406
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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 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 map$ (M,N;f)\to N$ is zero on the rational homotopy groups of even dimension.

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Yves Felix
Affiliation: Institut Mathematique, Université Catholique de Louvain, 2, Chemin du Cyclotron, 1348 Louvain-La-Neuve, Belgium

PII: S 0002-9939(2011)10763-9
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.